Hi krd67,
This has become a very difficult problem to diagnose and repair. Standard procedures in such a case have not been successful, so we need to try some other alternatives. Doing scans for infections as recommended by Richard above is the best next step at this point, so please do that first and if you find and remove anything significant other than tracking cookies, check to see if that resolved the problem. If anything is found that was not cleaned or could not be cleaned, then post back with that information and proceed no further until we've had a chance to consult our security experts about that infection.
What other tasks are scheduled in Task Scheduler and are they occurring when they should with no problems? You mentioned earlier another task that also wasn't working - please refresh my memory as to what task that is exactly. If those are the only two, and neither is working (or there are more and they too aren't working), then we need to consider the possibility there's a problem with Task Scheduler itself. If there are other tasks that are working, we need to try to figure out why some work and others don't - in effect, what makes the ones that fail different from those that succeed.
First, let's try a simple approach. Let's create a new task to manually defragment the C:\ drive every day at some time when the computer will be on but you aren't likely to be using it (and not at the same time as any other scheduled task). In Task Scheduler, on the left, select Task Scheduler (Local) / Task Scheduler Library / Microsoft / Windows / Defrag and choose the ManualDefrag option (not the scheduled defrag option). Click on the task and then in Actions, click on Properties. Set it up as indicated - use the previously-provided tutorial if you need help setting up the Task properly. Then let's see if the task runs according to schedule. If so, then we can probably rule out Task Scheduler itself as the cause of the problem. If not, then we need to examine Task Scheduler much closer to see why this task also did not run and that suggests Task Scheduler is, for some reason, not functioning or having some type of problem.
In the meantime, go to Start / Control Panel / Administrative Tools / Event Viewer and check for errors involving task scheduler or scheduled tasks in the System or Application sections. Task manager should give you a history of attempted tasks (and whether or not they were successful - look for those that weren't successful) and that should help you find the events based on the time of those scheduled tasks and what the task was. When you find the errors, click on them for more information and then click on the Details Tab and copy the contents and paste them to your next post. This may help identify the cause of the problem. Try to provide several different examples if there are different tasks or if one task shows different detailed information in different errors.
I hope this helps at least identify the source of the problem so we can focus our efforts - otherwise, we may need to do some broad, generalized troubleshooting.
Thanks and good luck!