You will have a really hard time trying to find any 4GB dimms that work in that board.
It only works with low-density DDR3 1333 made for up to LGA1156 (H55/H57) chips, the kind that hasn't been made in more than five years. Back when DDR3 was new and ridiculously expensive.
In general, if the memory advertises compatibility with Sandy/Ivy Bridge (P67/Z68/Z77 etc) then it will not work in that board.
BTW ICH7 also doesn't support AHCI, but it is the last Intel southbridge to natively support IDE!