Which version of Windows is that?

Windows 7 Pro

I would try running Thunderbird in Safe Mode, just to rule out any add-ons that might be interfering.

I've seen some worrying trends. In Windows 10, we no longer have easily visible "frames" round windows and panels and this can make grabbing these sliders or the edges and corners very difficult. It's something to do with designing for touch screens. :-/

But you have Windows 7, where this wasn't such an issue.

Have you tried pressing F8 a few times? This will collapse and then open the lower pane. Doing this might re-set its height to something closer to normal.

I ran Thunderbird in safe mode and could move the bar normally.

I restarted in normal mode and deactivated the add-ons, extensions, dictionnaries and plug-ins one by one until there was none and the problem is still there.

F8 does collapse the lower pane but if I try to grab the bar when its at the bottom of the window F8 stops working.

Ah. The other thing that happens in safe mode is the disabling of hardware acceleration.

You can switch this off and on here:

Tools|Options|Advanced|General→Advanced Configuration

I verified and hardware acceleration was not activated. I tried with and without, no change. I hope you're not running out of ideas!!

Running a different theme? Safe mode disables those too I believe.

Nope! Using default theme.

Here is an article that describes safe mode and what it deactivates. Maybe something there will help. http://kb.mozillazine.org/Safe_Mode