2004 s-10 blazer......Electric latch quit working on tailgate glass with it closed. Makes a whiring sound when button is pushed and dont unlatch. HELP

 

There is a plastic piece between the solenoid and the latch that often breaks; sounds like this is what has happened in your case. There is a way to get the glass door open and the drop gate open, so all can be fixed.

Do a search here for "how to open a stuck rear window-tailgate"

 

Regrettably common problem, they used a cheap part that's prone to failure. You need one of these: https://amzn.to/3mRcvOi

And replace it by doing something like this:
There are various other guides here if you do a search too.

Getting that tailgate panel off is a pain though, you essentially have to break a couple clips to do it. I would up using a hole saw to cut an access hole so I could actuate the lever manually, then covering it with a sticker. It's old truck anyway, don't care, and now my lift glass works again.

 

No need to do the above video to get the glass door open...follow the steps shown in the "How To Open A Stuck Rear Window". This gets the glass door open without breaking anything.

Now if the tail gate latch is broken...that is a different problem.