Did the motherboard come with the new case? If so, it could be faulty in some way (AGP), unless you are using PCI, in which case... it could be the same thing. Try switching back to you're old motherboard in that case
Does your new case come with a psu? Cuz you might have to use the psu from your HP comp and switch it to your new comp to get it working. Thats what Dell does, they force you to use specific dell psu's or it wont turn on at all.