I'd recommend starting with a good inspection inside the tower.
For starters, what kind of hardware are you dealing with? Old (four years or older) system? Hard drive(s), SSD(s), or some combination? What's the machine's environment like, dusty, damp, pets nearby?
To inspect the inside of the tower (this may go against a typical tech inspection, but you're only going to be looking for trouble) start by unplugging the the power supply cord at the rear of the tower, if you see a power supply switch turn it off as well.
Set the tower on it's side and remove the screws that hold the side plate in place, then remove the plate. At this point, touch the main frame briefly, this will ground any stray static charge and you and the tower will be grounded to the same potential.
A small flashlight is handy for this step. Closely examine the condition of the mother board and the installed cards (RAM, GPU, etc.). Things to look for are signs of arcing or high heat, dust, cob webs, lint, pet hair, etc. Also check on the mother board for small "can" type capacitors. If the caps look like they have been "over-inflated" and look ready to burst, make note of that. Also look for signs of damage or arcing.
Next, check the cables from the power supply to the mother board. Look for signs of charring and check for good contacts where the cables meet the mother board. A slight push on the connectors may reveal a loose cable. Now is also a good time to inspect all of the cooling fans/heat sinks and clean off any dust.
Next, check how well the RAM and GPU are seated to the mother board. They should feel tightly seated (not loose).
Next, try to get a good look under the mother board and inside the power supply. Look for dust and lint.
If everything looks good, now might be the time to change the battery on the mother board.
Its an old field engineer trick that saved my backside many times. Newer mother boards are more immune to a dead battery, but that battery can still cause trouble and you've already got the case opened. Plus, batteries are cheap.
Assuming everything looked good, set up the tower again and plug in the power supply but leave the side cover off. DO NOT TOUCH the mother board or the inside of the tower when the power is applied. Now is also a good time to re-seat all of the connectors to your peripherals (key board, mouse, monitor, wifi dongles, etc.). This might sound dumb, but a bad joystick connector kept me at a customer's house four hours more than it should have.
Start the computer while watching the mother board.
Look and listen for signs of trouble during start-up. If you are running hard drive(s), are they making a ticking sound or a loud "whir" during start up?
Are all of the fans turning and running quietly? If you are running SSD(s), are any small LEDs turning on? Look for signs of obvious trouble.
BTW, work to YOUR level of comfort. If diving into your tower sounds like its over your head, don't try to force the issue.
My gut says you've had a hard drive or SSD failure of some kind but there's no way I would commit to that without seeing the machine start up.