My daughter has a portable CD player from some no-name company I've
never heard of (got it as a gift).

It has started not playing. Put a CD in, close the player, and there
are these soft klunking noises from inside, like the disk is slowly
trying to spin. This lasts maybe five seconds and the spinning stops.

I have tried several CDs and new batteries in the thing, none to any
avail.

Is there a simple fix, or is it time to chuck the thing and buy a new
one from a known manufacturer?