Why can't old PCs view modern sites?
As of 2019, and a few years before, there's another factor. Any modern, secure site would have some flavour of TLS encryption, and be hosted over HTTPS. The browsers of yore as linked below probably would simply not be able to load many sites - even 'simple' ones without some intermediary (See this example of a slack client for windows 3.11 ).
Simply, a lot of modern HTML features we take for granted did not exist back in those days. There are attempts to build 'modern' browsers for older OSes - classilla, for example. You can easily load up linux onto a suitable PII or PIII system and still be able to handle a basic modern webpage.
On the other hand
This is google on OS/2 warp 4.52, on a VM on a modern CPU. I could replace this with linux and the same page would render correctly. If I only could find a modern browser of some sort, I'd certainly be able to render this very simple page. Opera might work
Same page, different browser (opera 5.2 I think), and it works gloriously here. It breaks down to newer browsers support far more than older ones did. If you could get a 'modern' browser to work, it might render things better - SE chat breaks down for one - and its a modern HTML5/Ajax based website.
Naturally I have neither flash nor HTML 5 there, but you get the idea. Its all about the browser
The answer is the internet simply uses more resources on a computer. More CPU processing, more RAM, more disk I/O, and newer instructions required by the OS. It is not one thing, it is all things that a modern browser can do that end up taxing every aspect of the computer. (Open a static html site and I bet the computer will be as fast as ever; but what sites are static these days?) One thing like too little RAM can cripple a computer, but you overload 2 or 3 things at a time and you have a computer that for all intents and purposes doesn't work at all.
An older computer CAN be used, albeight slowly. But you need to make sure it is not being overloaded by simply keeping the OS running AND has extra resources availible to actually browse. What is your baseline specs with no programs open? And the PCI bus can be your friend for upgrading things like your disk and graphics. Here is what we have found works for us to use older hardware in modern times.
CPU - If your baseline CPU usage is 50%, then you have very little left over to run anything else. You need to make sure you stop all unneeded services, and stop all backround programs from running. And if you use active virus scan like AVG, you are pretty much screwed on being productive; nothing can be running in the backround.
RAM - If you have 512MB ram and your baseline RAM usage is 300mb, then you will be using swap space to browse which means your computer will run EXTREMELY slow; this one thing alone can cripple ANY computer. I have seen my browser use 1-2GB alone. Watch your RAM usage at all times to make sure you do not use swap. Also, install as much ram as you can, and make sure it is as fast as it can be (PC-66,PC-100, PC-133?)
Disk I/O - Count the files on windows 7 vs windows XP vs windows 98; windows 7 has exponentially more files it uses. Since seek times are the biggest slow down on a platter style drive, you will for sure have very slow disk read rates because of the slower seek times AND the additional files accessed. Condense your OS partition so it is not more than 20% free (make it smaller if it is) and defragment using a third party defragmenter using a smart placement or defrag by access times to minimize the head movement in the drive. If you can, get a PCI SATA controller and use a modern 10K SATA drive like Western Digital HLHX series drives (fast and cheap on EBAY).
Graphics - Get as modern a PCI or AGP graphics card that you can to take a load off of your CPU. I have seen single tabs in my browser cause one of my cores to run 75% or more (Athlon X4 630). While a graphics card will not help on all pages, on some pages it will.
Network - Use a dedicated NIC to take a minimal load of your CPU, although you probably already are on that old of hardware.
Sound - Use a dedicated sound card to again, take minimal load of your CPU. Although some don't help with this.
Resolution and bit depth - Drop your resolution and bit depth to 16 bits to help take a load off your MB, CPU, and possibly RAM.
MB - Don't forget your northbridge and southbridge have limited bandwidth that will also get eaten by overhead, so reducing your overhead could help keep things so your MB itself isn't slowing things down.
OS - It is possible your CPU cannot even support the instructions needed for a modern Microsoft OS's; making a move to Linux could also help greatly for this reason, and it will reduce your overhead on your CPU, RAM, and disk.
We used a PII 266 with 256MB RAM 7 years ago and 256MB was max RAM. That alone crippled the computer. The next computer was, and is, a P4 2.8 with 2GB RAM that my wife refuses to get rid of because it runs as fast or faster than most people she knows and why fix it if ain't broke. But we apply many of the things I have mentioned above to keep it running fast. No background programs (not even virus scan), condensed partition size, defragment by access times, business class 2D PCI graphics, and 2GB RAM. The computer stutters on high resolution videos and some sites slow it down, but rarely. Other than that it is used everyday for average office like activities.
If you can't get enough RAM, you don't have adequate disk I/O, your CPU usage is 60% idling, and your CPU doesn't support the instruction required, you will be crying because of how slow browsing is and the errors because of it. But address ALL those issues first, and any other second, then you should be able to make it work.
I have a 9 year old P4 desktop at home, with Ubuntu 12.04 installed. It has a 500GB hard disk, 3GB RAM, and a 512MB video card. I use it as home server, for backup, file sharing, and for batch scanning negatives. I don't know how it would work with XP now, but I suppose it would not make much difference in speed.
It can do almost anything. YouTube videos work. Some videos don't work properly, probably because the resolution is too high. Most sites work, although it takes a bit longer. Doing two things at a time may take a while... I can even start up VirtualBox and run Photoshop in it. That really works, although sometimes I have to wait several seconds. Wait for each action to complete. Close everything else, especially Firefox with heavy sites in it.
So how does this relate to your situation? This is a P4, so two generations later, but still 9 years old.
My guess is that Windows gets slower with all updates. I cannot prove that, but it's my gut feeling. JavaScript in websites is much more complex. Think of jQuery and what it can do. Browsers can handle PNG transparency. CSS3 and HTML5 require more power. Do you use add-ons? Antivirus? Antivirus from 10 years ago required less power I suppose. Now there are all these different kind of threats and the antivirus program has to scan for them.
There is not one reason. It's the whole package. Not only more memory, but faster memory. Hard drives have faster connectors.
Your old computer may need a system that requires less in the basis, like Ubuntu, Debian or Centos. Maybe that makes it more acceptable, but maybe it doesn't make much of a difference. You can only try. Ubuntu is the most fancy for desktop usage, the others have less bells and whistles, but do the job.