Firestone is a car place in the US that does a full inspection of your car; incase your car sat around without being driven for years. They check the tires, fluids, brakes etc etc. They call this a 'Complete Vehicle Inspection'
Is there a similar 'Complete Vehicle Inspection' that can be done to Arduinos that have been used a lot and were sitting around for years and has dirt collecting on them?
Is there a procedure to perform ''Complete Vehicle Inspection'' on an Arduino where we can check that the oscillator is putting out the right frequency, the pins are out putting the right voltage etc etc?
Well, my first suggestion would be to consider the investment. A car would be worth many thousands, perhaps tens of thousands, of dollars. Your Arduino, not so much. If you want an Arduino with the best chance of success, buy a new one.
Beyond that, well, yes, you could do some selection of:
test all digital pins as inputs and outputs, verify pullups still work, etc. Requires you write code to output results to Serial monitor, and with a little work you can verify that the RX pin works, too.
exercise all analog input pins through their range
verify clock frequency
test I2C and SPI functionality
visually watch for all 4 LEDs working, including the pin 13 LED if you code for it
verify 5V and 3.3V outputs work (will require an input to the DC jack, otherwise 5V is just whatever your USB connection is giving you).
There's probably more, but that's a start.
But quite frankly, for me, dustbin and new purchase would be a better move, unless you've a large stack of Unos from some old course work that you want to vet before handing out next semester.
In another thread where an instructor had this question, I suggested it would be a good assignment for that 'bright spark' in his class - the kid otherwise bored out of his tree could come up with a test code and wiring strategy to vet the Arduinos his class had just finished abusing. It's a thought, anyway.
As a practical matter, if the Blink LED Example works, the odds are that the board is 100% OK
Where I work we make several microcontroller based boards & products. Every board has a special test fixture (sometimes a special board, sometimes another one of our products, special cables, etc., and in one case an identical known-good board). Some of the procedures use a multimeter or 'scope. A few products have a software-controlled multimeter.
And there is test software for each board/product to test all of the input-output pins/ports. The test program runs on a computer, not in the board's firmware.
I assume the Arduinos go-through some kind of similar test at the factory.
If the board voltage regulators, we'll measure the voltage(s). We don't routinely check the clock, but a lot of out boards have RS-232 & RS-422 and those ports will fail if the clock frequency is wrong.
Every board we make also has a self-test (POST) that runs every time the board is booted to test the RAM & flash, etc. The on-board LEDs can show a pass or an error code, but more often if the self-test fails, the self-test won't even run.
That probably doesn't make sense for the Arduino itself since the FLASH, RAM, and EEPORM is built-into the microcontroller chip and is unlikely to fail without the whole chip failing. But, I make sound activated lighting effects and they all run a power-on self-test that sequences the lights to make sure the lights are working and that they are being correctly controlled/addressed. (The sound input doesn't get checked until the thing actually starts running.)