The OP's problem implicitly raises an interesting point.

We don't think of IC circuitry (as opposed to discrete) as drawing a lot of
current. Nor do we think of it as being able to pull enough overcurrent for
a long-enough period -- without being damaged -- to pop a fuse.

Most electronic equipment has a fuse on the line side of the power supply,
and some has fuses on parts of the circuit that draw or pass a lot of
current (eg, an output stage). But I don't remember seeing fuses directly
protecting circuitry that's mostly LSI (or even SSI).

How often are fuses used in such circuitry?