Okay, well it just might suit your budget and your needs to upgrade to an AGP card, although I wouldn't want to spend too much at all. Here's some comments I have from your post:1)
If I were you, I would only bother upgrading to 2GB RAM, as 32-bit OS can only "see" (and therefore, use) about 3.25GB meaning the rest would be sitting there unused. (i.e. waste of money). If you have 64-bit, then it will see all of it. 2GB should be plenty enough, though, because more RAM does not
equal a faster computer. It just allows you to do more things at once (or run big applications easier). If you want your computer to go faster, consider getting faster speed RAM. For example, if your motherboard supports PC-3200 (DDR 400) RAM at the fastest, check and make sure it's this. Do you have 2 slots or 4 in your current motherboard? If you have 2 slots and both are full (2x512MB sticks), then I really wouldn't bother upgrading this at all, as you're going to have to chuck them and purchase 2x1GB sticks.2)
If your hard drive is a Samsung, go to the Samsung website and find the drive test utility (under the support section). You can use it to create a bootable disk which will check your hard drive - if any errors are found, your Samsung is faulty. If no errors are found, then it's likely your hard drive is fine and the problem is somewhere else. Why do you "think" your hard drive is on the way out?3)
Power supplies... One of my favourite things to pick up on... If you say it isn't that great, then it's not.
Without a good power supply, many problems can and will go wrong. If you are going to upgrade your graphics card, it will require more power, and most of the time when people upgrade, it pushes them over the limit and it causes all sorts of problems. Unfortunately, I can only recommend that if you run any more upgrades, your PSU should be the first one. Without a good power supply, your computer will only make a fancy door-stop.4)
And of course, the graphics card. If your budget is around $200 for the graphics card, I would look for an Nvidia 7600GT or an ATI Radeon X1650 Pro. A quick search reveals that these can be found for around that price, but if you're in the middle of nowhere, it could be a bit tricky for you to get your hands on one at this price. One of these should give you reasonably good performance, and definitely would be a nice upgrade.