SkyDrive Stropped syncing, checked – everything seems fine, still doesn’t work

I read everything I could find on the issue on the web, checked every possible problem - everything seems fine. 

I have space on the disk, there seems to be no login/connection problem, the file names are fine.

However, SkyDrive is stuck in "Looking for changes" mode and doesn't sync.

As a test, I created a Test.docx file in Skype Drive folder on my hard drive. It's been 5 hours, and it is still not synced. 

It takes seconds for Dropbox to update files. Sky Drive has always been a bit slow, but now it just doesn't work at all. I see files synced up until about a week ago. No changes since then - and I still have 42GB free (total 107GB in my plan). 

Also, the list of PCs available for fetching files shows all 3 of my connected computer as "not connected" most of the time. 

However, my main PC is shown as available now, yet the Test.docx file I created 5 hours ago on this machine is still not synced. So the problem may be something else entirely. Fetching files may be just another bug. 

Notably, when I access the machine via Fetch Files function from Sky Drive in web browser, I see the files that don't sync. However, these same files wouldn't sync to the cloud. 

Any suggestions? 
Thank you.