assuming you have 300 to work with... maybe you can go with something like this?
Motherboard Bundle - Intel Pentium Dual Core E2160 1.86GHz LGA 775 1GB DDR2 667 Intel G33 Motherboard Heatsink And Fan : mbb-e21633
gives you the mob, cpu, ram
Maxtor DiamondMax 21 ATA100 250GB 8Mb Cache Hard Disk Drive <11.0ms 7200rpm - OEM : max-dm250p
you current HDD is most likely IDE, so you would need a new one, since this mobo only has one IDE slot, and that will be for your optical drives.
Jeantech Titan Midi ATX case, Front USB/Audio/Mic, **NO PSU** : jea-titan
simple case, but with better cooling than you probably have already...
HIPER 350 WATT 18db Silent PSU ATX : hyp-4s350
of course you need power to run it all...
depending on if you 6200 is PCI-E then you won't need a video card, but since you won't game, then the onboard graphics should do... if you wanted, and have enough left, then you might even be able to add a second 1GB stick of ram... but I wouldn't think you'd need it right now.