Why are my dwarves starving when there's food available?

A few things may be preventing your dwarves from eating the available food or drinking the available alcohol. The main two culprits are:

• No path available to the item or its container.
• Dwarves aren't permitted to travel where the food and drink is located.

Other things that stop dwarves from eating and drinking:

• The food isn't edible to dwarves. Examples: Seeds
• The drink isn't drinkable. Examples: Milk (shows up as other in foodstocks)
• The item is forbidden.
• The food or drink is claimed by a militia member as part of his/her food rations.

The dwarf fortress wiki has extensive articles on how to grow food, how to collect plants to eat or process (ie, cook in a kitchen) into edible food items, how to set up a still, etc. I'd suggest you look up plant collecting, still, food stock, and above ground farming. It is possible to farm underground, which uses a different set of plants (they can only be found in underground caverns or traded for with dwarven caravans) and requires easy soil layer access or making mud which sounds like it would just be an extra complication for you at this point in your dwarf fortress experience.

I've tried everything here, and I encourage everyone else with this problem to do so, but my problem seems to be caused by either a glitch or a limit on the pathing system.

I did find a solution: as long as the object the dwarf wants is very close, especially on the same z-level, the dwarves will be able to find it. I'm currently starting a new fortress based on this solution, and it's working well.

It's possible that most experienced players are already doing this to make hauling faster (and other benefits). If so, it would mean that everyone has the same problem, but they didn't recognize it because they already solved it.