Yea, a new machine definitely.
For pretty much anything but rendering, AMD simply beats down Intel, and nothing can change that. AMD really shines in games too, so AMD is definitely my choice here. If you can, $190 will get you a very powerful AMD Athlon 3200+ Venice Core. These are VERY quick processors that will easily run any of today's games.
RAM is a critical component too, $85 will buy you a quality pair of 512MB sticks (1GB total) which you can run in dual channel.
Anyways, for a new graphics card, you'll probably want a Radeon 9800 Pro or 6600GT video card. Those will run roller coaster tycoon 3 perfectly. If you want to go even further, a radeon x800gt is just around the corner too.
If you really are going to get a new machine though, think about motherboards carefully. You can find some cheaper $90 ones that will run perfectly, but you'll have to be careful in your selection. If in doubt, register at the anandtech.com forums and ask. They're very helpful.
I'm guessing you'll want a power supply too of course
. A 420W power supple of GOOD QUALITY would do you fine. Antec and Enermax are a couple of the very high quality manufacturers.
Any case would do I guess...even your old one. Again, if in doubt, anandtech's members are always willing to help out.