What kind of motherboard would be compatible with my Gateway GT5622 Computer?

most "BIG NAME" manufacturers customize the motherboard and case so that you cannot put someone else's stuff in the case when you are done with them. The do this by not aligning their ports to standard positions and using addon riser cards for slots and the such. You may be able to find something that would fit in the case but it would just be easier to buy a cheap case from anyone else.