I'd think your best bet for fixing this is to take the paneling off and going at it from behind (no pun intended). Take the paneling off, push the drywall back out, take several 1 x 2s (longer than the pushed in area is tall and, screwing in from the damaged side of the wall, screw the damaged sheetrock to the 1 x 2s. The purpose of the 1 x 2s is to give the damaged sheetrock something to grab on to. Make sure you screw into the 1 x 2s not only in the damaged area but also screw the 1 x 2s into portions of the wall that extend beyond the damaged area. This way the 1 x 2s are held firmly to the wall. Yes, you will still see some cracks on the damaged side when you are done and you will obviously see the screw holes but if I understand you correctly, you're looking for a quick, temporary fix.
To me, I think the bigger hassle will be trying to blend in (eventually) the texture. That's a heavy texture (ie, very noticable/many definite contour lines) and won't be easy to blend well. You may have to skimcoat the entire damaged wall and then try to replicate the existing texture on the nearby walls.
Good luck.
UPDATE: On second thought I wouldn't try to fix this by coming at it from the rear/undamaged wall. You'd have to tear off/re-install the baseboard for that, which also includes re-caulking and re-painting. I'd just go ahead and fix it the right way now, ie, just do it all now. Use a sharp utility knife and cut the damaged sheetrock out along the crack lines (if you're lucky maybe the entire damaged area can be cut out as one giant piece), screw the 1 x 2s in behind the open damaged area (I'd go with at least 3 vertical 1 x 2s (no horizontals), extending the 1 x 2s above/below the damaged area at least a foot so the 1 x 2s can be held securely to the sheetrock), then screw the damaged piece(s) of sheetrock back into place making sure you screw directly into the 1 x 2s you just installed. Again, you'll still have cracks and will most likely need to skimcoat/sand the entire wall and then match the texture and finish off with paint.
To me, I think the bigger hassle will be trying to blend in (eventually) the texture. That's a heavy texture (ie, very noticable/many definite contour lines) and won't be easy to blend well. You may have to skimcoat the entire damaged wall and then try to replicate the existing texture on the nearby walls.
Good luck.
UPDATE: On second thought I wouldn't try to fix this by coming at it from the rear/undamaged wall. You'd have to tear off/re-install the baseboard for that, which also includes re-caulking and re-painting. I'd just go ahead and fix it the right way now, ie, just do it all now. Use a sharp utility knife and cut the damaged sheetrock out along the crack lines (if you're lucky maybe the entire damaged area can be cut out as one giant piece), screw the 1 x 2s in behind the open damaged area (I'd go with at least 3 vertical 1 x 2s (no horizontals), extending the 1 x 2s above/below the damaged area at least a foot so the 1 x 2s can be held securely to the sheetrock), then screw the damaged piece(s) of sheetrock back into place making sure you screw directly into the 1 x 2s you just installed. Again, you'll still have cracks and will most likely need to skimcoat/sand the entire wall and then match the texture and finish off with paint.
