I see online that a suggested fix is indeed adding "Local Service" to the Administrators group. That certainly strikes me as a nice way to compromise the security of your PC's services.
Better to try and find a cause rather than resort to that.
Have you installed/changed anything since it last started OK?
Does the event log contain any associated errors that could offer clues?
Have you sent the error report to MS to see if it has suggestions?
Are there any non-MS services currently set to use Local Service as their account that could be to blame? Open Services.msc, and click on the "Log On As" column to put them in order so you can find the Local Service ones. Are any that should be running, not running? Or is it just "COM+ Event System"?!
Is your PC fully patched? If this error prevents you updating it, you could always put the workaround in temporarily.
Are your drivers up-to-date?
Rather than faff too much, you could always just use System Restore to when it did work...!