Well, if you are really on a budget, you can probably get by with just upgrading that ancient video card and get some extra RAM. You can get 4GB of DDR2 for $70 (pretty expensive compared to what you can get with the current DDR3 RAM prices, but cheaper than new motherboard+processor+ram). Then just get new graphics card that you can fit in your remaining budget. You should be able to get a decent card if you can spend ~$150 (like an Nvidia 650 TI 2gb card, or AMD 7770 2GB card... personally I prefer the Nvidia due to their much superior driver support). You might have to worry about your power supply upgrading to a powerful graphics card though. Most people will recommend a 400W power supply for either of the cards I listed.
But it is true that your system is pretty long in the tooth. It just depends on if you have the budget to properly upgrade at this time or not. A new motherboard+CPU+RAM is gonna be in the $400-600 range depending on what you get, and will almost certainly require a new power supply (another $80-100), and then the video card as well.
Depends on how much you're willing to put towards an upgrade and how much you care about the game. From having played it a decent amount, the game is an awesome adventure up to 80 but then just doesn't feel like an MMO. It's got great story, but it feels and plays out like a single player game with an MMO element added on to it. They've been adding new content quite frequently since I stopped playing but nothing to change the core fact that once you're 80 there's not a whole lot to do aside from farm out some shinier gear.
Don't want to bust your bubble but a new PC would be your best bet especially if you want to enjoy "new" or recent games with resonable performances.
A nice gaming box (everything except monitor, keyboard, mouse, speakers and maybe the case) would cost you anywhere from 400 to 800 depending on your screen resolution and what you can keep from your current PC.