Still having the problem with Error code 0x800705aa.
I ran sfc /scannow (in Admin console) and received:
Beginning system scan. This process will take some time.
Beginning verification phase of system scan.
Verification 100% complete.
Windows Resource Protection did not find any integrity violations.
I have 3 partitions on my harddrive, and the one with the least amount of space still has over 50GB of space. The computer has 16GiB of memory.