I'm in search for an upgrade for my PC for a new CPU and a new HD. It was originally a single core 1.79Ghz (Amd Athlon XP 2200+), 256 Mb RAM (DDR 333), HD 40 Gb and VRAM 32 Mb. Now it is a single core 1.79Ghz (Amd Athlon XP 2200+), 1 Gb RAM (DDR 333), HD 40 Gb and VRAM 128 Mb (ATI Radeon 9200SE). I want a dual core of min 1.5 Ghz and a second HD of min 40 Gb.

I don't see any reason why you can't upgrade your hard drive by buying one from BestBuy or WalMart. Just make sure you have the correct type. You can take the old one with you, either EIDE or SATA is needed, they will be able to tell you which one.

It'd be easier to find a processor for you if we knew which board you have. Then maybe there is a compatibility list out there.

I don't believe you can add a dual core CPU to a single core motherboard. The sockets are different. This means you will need to replace the motherboard. Frankly, I wouldn't invest any money in this machine and buy a new one.