The first thing I would like you to try is a system restore. This could correct any files that got damaged during the 2010 uninstall.
To do this click the Start button, clicking All Programs, clicking Accessories, clicking System Tools, and then clicking System Restore.
Pick a restore point which was before the issue started if one exists. Do not worry system restore does not effect your personal files such as email or pictures. It only changes windows operating system files.
If system restore does not work the first time please try and earlier restore date.
If you cannot get system restore to work please download and install the following from microsoft:http://www.microsoft.com/download/en/confirmation.aspx?displayLang=en&id=5582
If you still cannot launch the program do the following
download this program, it is a better uninstaller than the one within windows and can get rid of left over file and broken uninstalls:http://download.cnet.com/Revo-Uninstaller/3000-2096_4-10687648.html
Once downloaded run the program and it will show you all of your programs.
Check carefully and see if Office 2010 is still there, If it is uninstall it with this program.
Also I would suggest you uninstall office 2007 as well.
Once uninstalled restart and you can try reinstalling office 2007 again.
If the above suggestions do not work please reply back to me to let me know. If it does work please click the accept button.