If you are an Administrator, it wont require a password (it already knows it), if UAC is turned on it would only require you clicking on the UAC request to run the program "Elevated".
Is sfc.exe located in System32, I suspect not, based on previous form.
Is your machine 64-bit by the way, your Handle suggests it might be?
Try running ChkDsk to check your drive for errors. Right-click your Drive icon/ Properties/ Tools/ Error Checking. Try it first by not checking either box (Read-only mode) to see if it flags any hard drive or file problems. If it does, start by ticking both boxes, in any further rerun.
What recovery options (CD, DVD's. Recovery Partitions, etc. come with this machine, we are heading into that area?
Under some circumstances it is possible to run a repair install and save your data, other circumstances only allow for returning to factory settings and loss of data, unless you save it beforehand, thus the question.
You still have the option of getting a sfc.exe (if it is missing) from an equivalent machine and placing it in System32 and trying to get it to run from the Elevated Command Prompt.