For many years almost all CPU's from Intel & AMD are 64bit capable
you can run both 64bit & 32bit versions of Windows on a 64bit CPU
Is your Windows Software 32bit or 64bit ?
The only significant disadvantage for 64bit versions of Windows Vista & 7 is lack of device drivers for old hardware such as multifunction devices, printers, scanners etc.
Have you upgraded from XP to 7 recently ?
Microsoft gives a free version of MS Virtual Machine 2007 which allows you to install Windows XP (for Home versions and Win XP upwards)
With Win 7 Pro, Ultimate & Enterprise you can download a free Virtual Machine + virtual disk containing a licensed copy of XP SP3
which maybe useful if you have old programs which do not work under Vista & 7
What is your OS? Almost all the processors for the past 5 years have supported 64bit memory extensions. The processor does really care if you are running a 32bit or a 64bit application as long as the OS supports it. Most likely the way to fix your problem is to use an OS like Windows 7 64bit Pro which will have a build in emulator for XP that will allow you to run your application in that environment.
Most of my software works with 32 bit. Now that I have a 64bit cpu, I can hardly do anything with my computer.
Can I have it physically changed or must I sell it and buy a 32 bit one?
You cannot "physically change" a 64-bit CPU into a 32-bit CPU.... well actually you can attempt to but it is almost a guarantee that you will damage the CPU. The chances of you dying within the next 100 seconds is higher than your chances of doing a successful homemade hack surgery on a CPU.