The HP motherboards are "proprietary". The screwholes in the motherboards are custom, and not an ATX standard (which most "normal" motherboards are). Your motherboards literally only fits these cases, of which a few are tower models:
HP Compaq 8200 Elite Convertible Minitower PC:
HP Compaq 8200 Elite Microtower PC
HP 8200 Elite Microtower
HP Compaq 8200 Elite Small Form Factor PC
HP 8200 Elite SFF
HP Compaq 8200 Elite Elite Ultra-slim PC
HP 8200 Elite Ultra-slim PC
HP Compaq 8280 Elite Microtower PC
HP 8280 Elite Microtower
HP Compaq 8300 Elite Microtower PC
HP 8300 Elite Microtower
They're all small (mini or microtowers) cases. I'm afraid you're pretty stuck to buying a new motherboard, as I'm sure the mini or microtowers are too small.