Fans spin heavily and chimes at boot up, but no picture

You’ll need to do a bit of cleaning! Both the fans and logic board are quite dusty.

Get a small soft paint brush to carefully scrub the logic board to loosen the dust and use some short blasts of can’ed air to blow the dust away. Using the same brush carefully wipe down the fan blades from both sides and again blow the dust away.

Looking at your pics I do see some areas in question but the dust is hiding things. I also see some signs of wetness on the insulator plate under the fans. I wonder if someone attempted to lubricate the fans. Your dust buildup could be worse do to oil vapor coating the logic board.

While not practical for most I would use an ultrasonic cleaner with 85% Isopropyl alcohol to clean the board fully for a few minutes. The other option is to use a loadable spray can which you pressurize with the Isopropyl alcohol and using a snorkel tube power wash the board to remove the oil film as best as you can and the dust that’s being held by it. Just be sure to do this in a well ventilated area and not near any ignition sources as both the liquid and vapor is quite flammable!

The areas I’m concerned are on the main logic board with is on both sides near the right side fan (on your left looking down from the bottom) where the GPU is located. The other is the port area again both sides. After cleaning take a fresh set of these areas both sides. Do make sure your camera is parallel with the logic board so the focus is clear across the full surface of the board.