Win7 Update hangs indefinitely on "Checking..."

My Windows update has stopped working altogether, it just hangs on "checking for updates", I've left it on overnight, still nothing. I've tried sfc /scannow (both in Windows and from boot), the readiness tool, running chkdsk /f /r, and the Windows troubleshooting fix. Also, every time I start up my pc I get two pop up messages:
Error: -3 from inflate incorrect data check
Error decompressing shell32.dll

I'm almost certain my HD needs to be replaced but I thought I'd see if anything can be done before going through that. I've attached the CBS log and the windows update log from event viewer. Any help is appreciated. Thanks.

Follow these instructions exactly.
First, set Windows Updates to never check for Updates.
Next restart your computer, then install KB3020369, if not installed.
Then install KB3172605.

Windows updates should return to normal. You can then reset your updates to automatically check for updates if desired

https://support.microsoft.com/en-us/kb/3020369

https://support.microsoft.com/en-us/kb/3172605

That worked! Thanks a ton.

You're welcome.