How do I switch the input for my monitor from DVI to HDMI from my PC?

I have similar situation with dual systems (Win/OSX) setup sharing a monitor, and I am lazy to reach out and press the buttons twice on the monitor to switch inputs.

The solution I'm using now is through AutoHotkey (https://autohotkey.com/). As shared by user shimapan in this post, you can customize the hot key that sends DDC/CI (from your operating system, in this case Win7) commands through connecting port (VGA/DVI/HDMI/DisplayPort) to your monitor.

The downside is that you need to have your computer on in order to send the commands.

I also have Synergy (synergy-project.org) set up on both systems, so I can use the same keyboard/mouse to control both systems.

Unfortunately your model of monitor (Acer P235H) doesn't implement any control protocol - such as an IR remote or HDMI CEC, so you won't be able to influence it's behavior with both inputs connected. That said, it's sometimes possible to trigger a change of input when a source is disconnected. That is - if you were to disconnect your laptop you may find the monitor will automatically fallback to the other input.

Connecting the Digibox to your PC won't work either. Most graphics cards (including your Geforce 210) are only designed to output images over the ports they provide, rather than take input data. This means if you do connect the Digibox to the Geforce's HDMI port, you'll be connecting two outputs together which won't work the way you expect.

A solution to your problem would be to purchase an HDMI Switcher. You could then connect a single display (your monitor) and each of your inputs (PC and Digibox) and have the ability to switch between them with the push of a button, or with a remote - depending on the switcher you purchased.

Further to this, you could get a USB Infrared Transmitter which you could install on your PC to programmatically send commands to the HDMI switcher, provided it came with an IR remote.