Keep it in a water tray and give it some time. Post a photo too if you would.

The messed up section to the right is the remaining mangled pouch. The tiny leaf is the new growth which is drying up at the tip. The other droopy part is possibly a leaf or a pouch... Not sure but I am thinking leaf. It had two pouches and 2 or 3 leaves with the small growth just beginning to take off. I have it outside but check it frequently. IF it survives, it and it's pal the Venus Fly Trap will get wintered in an unheated and CLOSED room where my son's Bengal cat can't get at them. South exposure so plenty of sun. Very angry at myself for not getting it out of the house sooner.

Just give it time, it'll probably throw new pitchers if the rhizome wasn't damage.

All the growth is shrivelled and brown. So how long should I wait for new growth, or before accepting it is dead?

Wait another month. If nothing by then toss it and get a new one.