Can i run windows professional 32 bit on a new win 7 64 bit computer

The compatibility issue will be with win 7, not a 64 bit machine.
32 bit software runs on 32 bit or 64 bit machines, I'm using plenty of it.
But some older programs do not run on windows 7, period. They WILL run on XP.
There is also a microsoft (3 part) download, "virtual machine" "XP mode" that is supposed to overcome windows 7 incompatibility, but I have tried it, and it did not help anything.
Among the programs that would not run on win 7, includes NERO burner software made for XP, printer and camera (canon and other brands including HP) software
that would run on XP. Several of these manufacturers have produced DRIVERS, but no software, that would run on win 7. I can still use my printer, but not the printer software. I can still download from my camera, but I can't use the camera software. My friend's HP printer will not run at all, even after installing an HP "update" that was supposed to make it work with win 7.

Then, keep this in mind when loading new software programs into win 7:
A. turn off the security antivirus and firewall.
B. load and install the software.
C. restart the computer.
D. Turn the security and firewall back on.

If you have installed free downloads, or any software that has promised to "fix" "speed up" or "clean" the computer, no wonder you are having problems. Don't ever install this junk into your computer, and if you have already, delete it all.

If you have installed free antivirus from a download, delete it and use a real professional antivirus, an all in one security system such as Panda, Norton, Kapersky....free antivirus can cause all kind of problems, especially when you load multiple security programs and run them all at once.

Finally, WHICH software is this? Contact the software manufacturer by phone, check the compatibility, or check for newer versions that were made for win 7. Check the manufacturer's website for newer versions of software.

But don't forget...FREE software can contain spyware and viruses. Including the software you are trying to load. Perhaps the computer security is rejecting the software, because it contains MALWARE. Just because students are loading it does NOT mean that it is SAFE.

Check Dell's site for XP drivers for your system. If they have them, XP will run on it. If not, XP "may" run but probably with issues. Unless you have a way to restore the system, don't even try with XP. Get a cheap used PC and run XP on that, $100 or less can get you a usable P4 system with XP.

Please be aware that, if you intend to install XP on that system in addition to Win7, installing an older OS after a newer OS is in place tends to lose your ability to boot the newer OS. There are a number of different ways to deal with this, if that is the route you choose to go.

1) Get another drive for XP and disable all other drives. Install XP. Plug in the other drives. At this point you have two bootable drives and choose in BIOS.

2) Wipe out your current OS, install XP, then install Win7. Usually requires a full Win7 disc, not the recovery disc that you get with most machines.

3) Install XP in another partition on your drive, then do a Win7 repair install.

First, see if it will run in compatibility mode. The other options can be a lot of work. Better yet, contact the software mfgr and ask if they have a Win7-compatible version.