This is a G2, not slide release pin. Hopefully, gun not loaded.
Does your barrel move at all (it's in wrong place for position of slide in pic - muzzle should be near end of grip frame). The slide release bar has to be pulled down evenly on both sides to release slide. If the slide is hitting solid and you can't bump it on something solid to break it loose (don't be afraid to use a bit of force), you may need to drive the pins out of frame to remove metal insert from grip along with slide/trigger to see if there is anything that you can see causing problem. Can't tell from pic if mag is in or out - should be out and you might look up mag well to see if anything causing can be seen.
No magazine or round in the weapon. It is stuck in that position in the picture. It won't budge but maybe a 1/4 inch back, I'm looking up into the magazine well and don't see anything it could be caught on.
AS somebody else mentioned. the barrel should not be slid back with the slide.
Either the barrel is busted ( barrel locking block ) on the bottom or you have an extractor arm or release assembly bent and jammed into the side or bottom of the barrel.
See if you can push the trigger forward into it's normal position - looks hung up in firing position - seems I read about this a while back on another similar pistol jam. Does the slide move enough rearward to see the firing pin? I recently had to remove the firing pin to get a slide to release on a PT24/7CA. If you don't feel comfortable doing anything, just send her back and let Taurus sort it out. They should pay for the return freight to & home under warranty.
I had the same problem with a PT11 G2. This seems to be a common problem with the 911/940. Look down the empty magazine hole and you'll see a small round button. Depress that button with a screwdriver, punch, w/e and you should be able to take the gun apart again to fix rod position.