Unfortunately these machines don't always use stock parts, and the bundle boxes from Compaq, HP, Dell, etc., are the worst offenders in using non-standard stuff. A typical back of the case fan is an 80mm, but there are many systems that use 90mm or 70mm fans, and some that use 120mm fans.
What I would do is open the case and remove the fan. It will be held on by four hex screws at the corners, at most, and will be connected to the motherboard or a feed from the power-supply using a standard two or three-prong plug. The three-prong plugs have a separate connector for sensing fan RPM, so if you have one of those and don't get a matching unit, your system BIOS may complain that the fan isn't working even when it is. Make sure you unplug the machine from the wall, and always touch the metal parts of the case prior to handling anything else inside.
Once you have the fan out head to Radio Shack or any local computer dealer and see if they can match it up. A good place to hunt one up online is Newegg.com.
However, I would not be surprised if the Compaq used a proprietary form factor for the fan. Either a non-standard diameter or non-standard thickness. In that case your only option is to call the OEM and order one if you can (and if they can tell you which one to order), or find a similar junk PC from the same MFG and remove its fan.