Several problems with these.
-Most common being the slots contacts losing their springiness resulting in poor contact to the cartridge. Takes about 10-15 minutes for me on average, replace is a better option.
-Dirty game contacts, most used copper contacts that can corrode over time. Clean with cue-tip, and rubbing alcohol. Make sure you dry it completely.
-Try another game leave the cart in the up position and move it around tiny amounts to see if you can get any image on the screen.
-Open the machine up, pull the 72-pin connector back off, use a green scrubby on the connector on the main board. Attach the connector and try to get it running without the RF shield in place. (Not required for operation, just clean video and FCC regulations)
If you still get nothing at that point it might be easier to find another system/mainboard. But you should be able to get something be it corrupted graphics, or the game starting to load the circuitry itself in these is extremely durable.
In the 20 or so I fixed I’ve only come across one I couldn’t fix due to physical damage to the sound circuitry, at which point they are common enough where it’s not worth fixing.
Take care when using abrasive cleaners and get it off completely as they can also damage the contacts. (Hence the don’t use alcohol warning on the back)
Blowing on the contacts is a bad idea for the following. It deposits moisture on the contacts on the cartridge, and over time accelerates the corrosion process. I want to smack whoever came up with that.
But overall, it’s going to be a combo of playing with it until it works. I’ve had better luck on fixed ones running the cart in the “up” position. Just leave the power on, play with the cart, and watch the TV to see if you get the game to boot. Once you get something hit reset, or cycle the power.