I'm making a big assumption here, namely that Compaq use "pure" power supplies without needing other cables to ensure a genuine supply is attached to the board (hello, Dell). You may be able to transfer the power supply to a new case however
Any ATX tower case will fit the motherboard in that case. If its a Pentium 4 or recent AMD, ensure you get a "P4 Ready" case (or other similar nomaculture). This will have the additional power cable needed by recent motherboards. If you're using the Compaq power supply, that won't be a problem.
You will also need the manual or at least the pinout guide for the Compaq motherboard so you can wire up at the very least the power switch, and preferably all the switches and LED's for the front of the new case.
Also, be very careful about case fans - a new case may not have as many (or any) case fans, and you'll have to attach them to the motherboard for power.