DF1871: Oblivion still has a number of known Problems&Bugs.
Guessing from your description&specs it could be

I.Direct Show/Codecs-filter conflicts, wrong version of codecs, missing/disabled codecs, enabled condecs that disturb
your game...
If this is the problem you can try a Codec Utility tool that allow resets,tweaking,failurechecks....or you enabe/disable codecs and look if something changes,,,maybe a massdisable and look if runs normal(&without sound/music)
or if you get a failurenotice from your game.

II. problems if used with a Joystick or controller+software

III.Oblivion had several problems with Win10, many people could run it only windowed, SecuRom did not work with Win 10(Should be no problem with gog:), etc....
I don't use Win 10 so i have no idea what problem you might have...but checking the Win10/Oblivion-Threads might give you a solution

IV.Software/service/appliction conflicts, esp. on Win 8.1&Win 10
You wrote you tried a reboot...disable your netconnection and try a clean reboot.

V.Your GForce FX-card(it's a old Problem so it should be patched but..who knows)
Obilivion used 2.0 Shaders that didn't work well on GForce FX cards..this could be solved by editing the Obilivon.ini or by using OLDblivion

Edit
...and now searching, for Win10 problems/solutions...i just found the list of known issues&solutions^^...
great...why not while i started wrtiting...anyway...here's the link so
you can take a look and check it yourself

[url=http://en.uesp.net/wiki/Oblivion:Technical_Support]http://en.uesp.net/wiki/Oblivion:Technical_Support[/url]

Hope you find a solution or..even better...play morrowind instead ;)