Serial numbers are far less useful than you seem to think.
And if you can’t figure out the spec despite having access to the bike, I don’t think having you replace the fork is such a hot idea.
You need to know how to transfer/install the crown race, how to size and cut a steerer tube, how to install a star nut, how to adjust headset preload.
Also, the hardrock being quite inexpensive to start with, a brand new shock is likely to cost more than the remaining value of the bike.
And buying used forks can be tricky.
It has an 1 1/8” threadless steerer. A search on the fork’s model name/number should give you the travel. Failing that, measure axle-to-crown.
You need to match:
- steerer diameter, for buying used - remaining steerer length
- for rim brakes, intended wheel size
- travel/axle-to-crown
I’d look at the Suntour line-up. Might be something rim braked there.