A 1999 computer may be AT standard (not ATX) and the power switch, power supply, mounting holes, chasis cut outs, etc won't work for the MB you are about to retire.
How to Tell / What to look for:
Does the power cord go into the case and run up to the front panel or does it go into the back of the power supply? If the cord runs into the power supply it is an ATX power supply (that's good).
Look at the backpanel where the connectors go. If the case is ATX there will be a removable rectangular panel that varies with each MB. If there is not a removable panel you may not be able to use the newer MB.
If the case and power supply are ATX next problem will be the size of the old power supply. In 1999 250W was a big supply. It may not be able to power a newer MB. Post the power supply rating (watts and the current ratings from the label on the side of the power supply (for +3.3V, +5V, +12V) and list all the equipment, RAM, CPU type/speed that you expect to run in the old HP case. We'll let you knwo if the power supply is big enough.
Video - does the HP have on board video or a plug in video card. If it has a video card, what type is the video card (PCI or AGP) connector? It may not matter since the MB you are retiring probably has PCI and AGP.
RAM - the HP might use SDRAM which is different from what you have now (DDR). On the bright side you will probably be changing your ram for the new MB (I saw the other post) so you will have a use for the older ram.
Cooling - the old HP may not have enough case fans to cool the newer MB and CPU.
CPU and CPU cooler - did you get a new CPU and cooler with the new MB? I don't remember you mentioning it.