Probably something like a crank position sensor. In other cars, they cause the same start/no start scenario. If the engine has a camshaft position sensor (probably has 2 if DOHC) those can do the same thing. Chances are, fiddling with the fuse was coincidence.
If crank sensor is failing, it'll just crank. If you have a multi-meter, check it's ohms AND check if it's shorted internally. Keep in mind, IF the engine is starting, it might actually show an OK reading. Ideally, you want to check it for internal short and wrong ohm reading when it won't start. Just unhook the sensor (key off) and probe the connector for the sensor (not engine harness-side). Engine heat/cold start can affect readings, especially on a failing sensor, so ideally, check it with engine cold, then check it after engine has been running (values might drift slightly, but should be close with NO internal shorting. Then check it again during a crank/no start. If bad, it should be way off or shorted.
Also, check the condition of the crank position sensor's harness. I had a '92 SHO many years ago that did the same thing, but it also would run erratic at times then stall, miss, etc.. Someone before me, had reattached the cam belt cover and pinched the cps harness, which was rubbing on the crank pulley, and wore off the protective coating, causing an intermittent short.
Also, just for the sake of easy, next time it just cranks, loosen your gas cap (let it sit in the threads loose or remove it and try cranking; should hear a whoosh if air goes in), then try cranking again. I had an issue with a '96 Mark VIII where the cap failed and wouldn't allow air in the tank, which creates a vacuum and eventually interferes with the fuel pump. Car would run fine, park it, then 5 minutes later just crank. Loosen cap, it fired right up. It was repeatable. Replaced cap and it quit happening. Had the car another 35k miles roughly. But timing is key. It needs to be in a crank no start situation then immediately crank and start with it loose to confirm, unless you can somehow monitor gas tank vacuum.