Hey, I've got some that I kept in the house and they look like that :( I think they are goners, BUT do not give up hope just yet. The corm is the important part, and may just surprise you.

seahorse
p.s. what kind of palm is in the first photo?

It's a t. fortunei, that I abused this winter by depriving it of adequate indoor light in too small of a pot without enough water. I just uppotted it and brought it back outside so it's getting happy now.

Your best bet is to feel down the length of the psudostem, if it is firm then just leave it alone, but if it feels mushy then cut it down to where it feels firm again.
That second pic looks like you have some growth, I would plant it up to see if it will throw pups.

I've tossed around keeping tenders in the garage, but after this winter, i noticed that the garage is almost as cold as outside (ours is attached). I'll be sticking mine (Basjoos) in the basement or just leave them in the mainfloor, if they don't get too huge this summer. Good luck, i see you've got some sprouts (tulips?) coming up there...me too!

Wherever you store them they must remain above freezing, especially if the roots are not protected with soil. A freezing garage is not the place for them. A very cool basement above freezing temps is OK.

Hey Bradleyo. I thought Musa Basjoo was hardy to zone 6. Just wondering why you didnt leave them in the ground, or is it not worth trying? (just curious)

Josh, it's not likely a basjoo. I bought it as such but the only ID I've gotten from somebody that seems to make sense is M. 'Rajapuri'. Here it is from last summer.

May:

{{gwi:405753}}

September:

{{gwi:405754}}

You can often loose all the stem and they still shoot up again from the corm provided that is not mushy too. Wait and see. Don't bin any of them yet!