its quite possible.
there is a product out there called the 'fix me stick' that you could plug into the old unit, run the program and then transfer the data that will take care of most viruses and other chit, good for home computers, not so great for business.
you can load the fix on the new computer after data transfer, just to be safe.
never used it myself, but know lots of people who swear by this thing for their home computers.
might be worth a look.