Does Hitachi UC14SD battery charger have a fuse?

Yes. You missed doing a simple Google search for "Hitachi UC14SD"

You missed the search result that would have led you to a nice parts diagram clearly showing a fuse clipped to the internal PCB.

http://www.toolpartsdirect.com/hitachi-uc14sd-charger.html

Fuse is item 3. It is a 6.3A, probably 20mm glass (probably) fuse - Amazed that you missed that!

You missed thinking wondering why, if the fuse had blown, what fault would've caused it to blow.

It looks like the charger is a relatively simple constant current charger, hopefully with some kind of endpoint voltage sensing. SHould be easy enough to trace the circuit enough to do some faultfinding once you know any transistor and IC part numbers and can look them up - oh, you don't do looking up, do you?

XXX
February 2017