Photoshop doesn't open files

...using Team Viewer to troubleshoot, the problem disappeared

You mean thru trouble never appeared?

How about reinstall / repair PhotoShop?

You can use Process Monitor to watch how PhotoShop behaves. It may give a clue. https://technet.microsoft.com/en-us/sysinternals/bb896645.aspx

Correct, when I connected the first time PS worked properly.
Reinstall and Repair didn't help (do they ever???).

Stabbing in the dark here, but I encountered a similar issue and it turned out to be dual monitor related.  When opening a program, the dialog was opening on the second monitor - which was no longer connected, but the program 'remembered' the window position, so it was opening off-screen.  
Expanding on NewVillageIT's idea, take a look at the local application log to see if there is anything useful being logged there.

Other things to check:
- Antivirus
- Firewall

- Check logs.
- Turn off protection temporarily.

No dual monitor here.

Btw all other Adobe programs work well.

Turned off AV protection, no difference.

Will try Process Monitor when I have access to the client's machine, although I have no clue as to what kind of hint I'm looking for.

- Start Process Monitor (PM) as admin
- Turn on Capture (no red X over magnifying glass)
- Open Filter (Ctrl-L)
- In Display Entries, change Process Name is WhateverIsNameOfPhotoshop.exe (I don't remember the exact .exe name)
- Pick OK
- Run PhotoShop (PS) and try to open a file.
- Examine the Results column for obvious errors, e.g. access denied and other errors.
- Toggle the various upper-right icons to control the number of events displayed (registry, file system, network, process thread, profiling). In your, case, just enable "file system activity" for now. You can toggle the others as you see fit.
- To further filter the PS file events, Open Filter (Ctrl-L). Set "Operation" IS, then add Open File or ReadFile

Thanks, will try.

check in event viewer if something is reported for photoshop
also - was there some things changed on this pc?  software installed - updates?

rolling back, or using system restore can helkp

Nothing changed. Will check event viewer when I have access to the machine.

Using Process Monitor, Besides Success I see these:

name not found
invalid device request
no such file
name collision
buffer overflow
reparse
path not found
file locked with only readers
no more entries
access denied
buffer too small
no more files

It may help to pare down the results you see.

- Add to the filter: Result is SUCCESS then Exclude.
- Save your current filter settings for ease of loading next time. Filter, Save filter...

Try to find suspect events pertaining to the PS file you loaded.

Update:
It seems to be a permission issue, from the hidden Administrator account it works fine. Any ideas what to do to make it work for the users (members of the administrator group).

Can a normal user run it by right clicking on the shortcut and 'Run as Administrator'?

No.

Can you do a malware scan with MBAM for example? http://downloads.malwarebytes.org/mbam-download-exe.php

The fact that it behaves normally when you help out with team viewer is a bit suspicious. Try a rootkit scanner like TDSSKiller if you can.

Which anti-virus do you have btw and is it up to date?

I can't imagine it's a malware issue. The problem began as soon as the system was installed. As I mentioned previously, from the super admin account it works fine.

>> I can't imagine it's a malware issue
But are you sure? What's the harm in doing a scan?

If I had easy access to the machine I would, but I don't. It's a clients.

You could try adding the user to the powerusers group.

Another thought: TEMP locations may not be writeable for that user. Try fixing security on C:\Windows\Temp as well as the location where variable %TEMP% is pointing to. This could be the reason why admin user has no problem and the user has.