When you were 32 bit was it also W7 or something else such as Vista or XP?
Generally most 32 bit software will also run under 64 bit but 16 bit software which can run on 32 bit will not run on native 64 bit, so are you sure it isn't 16 bit software?
What is the name and version of your software; have you checked the
compatibility center to see if your software is supported?
Have you tried installing in compatibility mode?
By any chance do you have W7 Professional, Ultimate, or Enterprise so you can run Virtual PC - XP Mode?