Dell Inspiron boot issues

Lights come on, fan starts spinning, but absolutely nothing else. Just a black screen.
No blinking lights, no beeps. Zilch.
I already pulled the battery, held down the power button for a full minute, tried every possible RAM combo... Nothing works.
Don't have an extra monitor lying around to test that.
Anyone got any other bright ideas?

Did you actually follow the correct procedure for a hard reset? You have to completely disconnect the power supply—unplugging everything from the AC adapter to any USB peripherals—then pull the battery out entirely, hold down that power button for a full thirty seconds, and then plug the adapter back in without putting the battery back in yet, just to see if it'll boot up.

Yeah, I did. But honestly, the fan is screaming and the CPU is running hot even when I'm just sitting there doing nothing.
I let it run for an hour just to see if it would actually boot up. This thing hasn't been cleaned once; it’s easily 5 or 6 years old now. It only kicks on once it gets hot enough. Been down this road before. Honestly? Probably not worth the fix... :@

Getting a professional cleaning and fresh thermal paste applied is actually pretty inexpensive at most repair shops, and if you’re comfortable popping the casing on a laptop yourself, you could easily tackle it at home. It should definitely help mitigate those overheating issues and might even make the boot process feel a bit snappier, though I wouldn't go so far as to say it'll be a magic bullet that solves everything once and for all. Why not give it a shot?

Not my laptop, but I'd tell the lady to just take it to a repair shop for a deep clean. I'm a software guy; hardware isn't really my scene.