Please answer the following questions, with the starting point of having replaced the fusible links at the starter solenoid so they are both known good.
Without turning the KEY ON, or trying to CRANK the engine.
1 - Turn the Headlights on, do they work? Were checking to see if Fusible Link B is OK which powers the headlight switch.
2 - Does the Horn beep? We're checking to see if Fusible Link A is OK which powers the Horn relay.
If both of the above work, that means the fusible links are both OK (which they should be if you replaced them both), since those two functions headlights and horn do NOT pass through the FUSE PANEL but are fed from different fusible links off the starter. Does your fuse panel, and fuses have power at this point?
If both of the above work fine, meaning both fusible links are fine then the next steps is to answer the following:
You say when you "HIT THE KEY" the fusible link(s) blows, do you mean it blows just when you turn the IGN to RUN or it blows when you turn the IGN to CRANK to start the engine?
This is an important question because we need to determine what is downstream of the fusible link that is blowing and might be your short circuit. It takes a lot current to blow a fusible link so that means, it has to be between the fusible link and any other point before it feeds the fuse panel and fuses. If it were something with a circuit breaker (aka windows, locks) that would(should) trip and not the fusible link. Everything that has it's own fuse protection from the fuse panel and beyond would just blow the individual fuse (not fusible link).
So at this point, you've blown the fusible link(s) you replaced that were working above (horn and headlights were working), and fuse panel has lost power, etc..
So now, try the headlights again, and blow the horn again...ONE or both shouldn't work at this point if either fusible link is blown again. Report back which doesn't work Horn, Headlights or both.
I think you have a problem in the Fusible Link A (Horn stops working) which also feeds the the IGN switch, fuse panel.
If it pops the fusible link when you try to CRANK the engine, please double check and be sure that purple wire to the Starter solenoid (from IGN switch) is not rubbing or touching/pinched near the starter. That will go HOT when cranking and could easily blow the fusible link if it's shorted, or the starter solenoid itself is bad.
Let's hear back on the HORN and HEADLIGHTS question with known good fusible links as you're starting point, and go from there.