|"Ever heard of a DDR2 motherboard with 3 slots?"|
No, not off hand. Are you sure it's not DDR1?
"I have no clue what this new board exactly is"
There *should* be a model number printed on it somewhere. Hopefully it's not an HP board...if it is, the model number will be M2N68-LA. It's based on an even older chipset, plus the HP BIOS is severely crippled.
HP and Compaq Desktop PCs - Motherboard Specifications, M2N68-LA
"Would this be better than my current board and does this other board support a dual-core proccessor?"
Can't answer that without knowing the make/model of your old board & the correct model number for your new board.