The first thing to try here is to manually remove the old version of Microsoft Office. Please do the following steps to fix the issue:
Step 1. Hold down the Windows key on your keyboard and press the R key to bring up the Run window.
Step 2. Type appwiz.cpl and click OK to bring up the program list.
Step 3. Look for the old version of Microsoft Office, highlight it, and click Remove.
Step 4. Look for any other Office products (compatibility packs, business contact manager, etc) and remove those as well.
Step 5. If the removals go smoothly please try the Office 2010 instillation again.