Is there any camera application that can save photos on internal storage? So my SD card reader is broke, and my only possibility of ever taking photos again is to use the internal memory.

The default camera option, says that no SD card was detected and if you press anything it closes. So I can't change path from there..

I have already tried camera360, but when I try to change the saving path, it doesn't do anything.

Other apps I've tried crash instantly.

If relevant, my device is a HTC Desire HD, rooted, with android 4.1 I think.
On the home screen, go to System Settings/Storage and change Default write disk to phone storage instead of SD Card.  This will solve your problem!