If the old software is 16-bit software then it cannot run in a 64-bit OS. This issue can likely be solved switching to the 32-bit W7 OS but I personally discourage this because 64 is the future and you are holding back your system (including limiting the maximum available memory to approx 3.25GB). Consider the Virtual PC or VirtualBox option instead (more on this below).
There isn't actually a lot of non-gaming 32-bit software that won't run in W7. If the old software is definitely 32-bit (not 16-bit that you just had running in 32-bit XP) then there is the possibility you could install this software as well as execute it in compatibility mode ... right click on the exe and edit the properties to run in the most recent OS on which it will function: example Vista SP2 or XP SP3.
If you are still having problems there is the ability to run a virtual environment ... basically under Windows 7 you can run a copy of XP (or Vista, or other OS). As firecat mentioned, Virtual PC - XP mode is a free download from Microsoft if you have Professional, Ultimate, or Enterprise (in this case you do not need a license for XP). If you have Home Premium or Starter or if you simply prefer it you can install Oracles VirtualBox (free w/ registration) but you will need your own licensed copy of XP (or whatever OS) to install in VirtualBox plus your hardware must allow virtualization.
Here was Microsoft's advice for Vista - it still holds for W7