Don't think you can do what you need to for 80 quid. To add another 512 mb ram and put in a better graphics card will cost maybe £120. (For Doom I'd recommend an Nvidia card like 6600GT or a 7600GS)
To be honest you second suggestion makes more sense. Flog the old one and put the money towards buying a core 2 duo based pc with a 7600 GT card and 1 GB ram.