You would need to check with the motherboard manufacturer to see what your particular motherboard is capable of. However, if it's a PII motherboard, it can definitely only support a PII processor.

Actually, that DFI motherboard will support a Slot-1 Pentium III, as will nearly all late-model mobos that use the BX chipset -- I'm not sure what the top-end PIII for that socket is (600MHz or more) -- as long as you update the BIOS, you should be OK. If you upgrade the BIOS, look for one that can overclock a bit.

Also be aware that the clips that hold the processor in the socket differ from the PII to the PIII and will need to be changed out before the module swap. Another possibility is a socket-to-slot adapter so that you can use a socket-style PIII or PIII/Celeron chip.

You have gotten some good replies. Here is a site to do some shopping.
http://www.pricewatch.com/
The older processors should be quite economical. Just try to be sure they are new and carry a valid warranty and return policy.
Buyer Beware! Happy Hunting.