As someone who has grappled with fairly severe depression, it's not that you have no desires. Your body does a decent job of making sure you maintain your body by giving you plenty.

I would merely say you have no rational desires. As a human your are functional, but as a rational human you've hit a wall.

I can't definitively say I've been depressed, but is it fair to say that you still have desires and want things, but it feels like there are insurmountable barriers between you and desires/things?

Yea, I think that's fair. I think it's also pretty subjective, so it wouldn't surprise me for people to experience it differently. But whatever is wrong or blocking one or one's desires (or whatever) is in one's brain, if not one's control.