If the disk spins up but doesn't work, the type is probably wildly wrong. A lot of these 386 SX/SL laptops use proprietary disk types, so you might have to pop the cover to look at the disk geometry itself.
My Compudyne 3SL/25 had the same problem - The 80MB hard disk spun up but was not detected. Some BIOSes don't have this feature, and some hard disks can't do it either.
Might be worth a try to just set the type manually at random and see if it comes up.
Very cool form factor, wonder how hard it would be to put a 387SX and a new battery in it? Would make for a great little portable machine, don't you think?
Too bad it has that weird LCD connector instead of a TTL or VGA output.