Repairing The Lynx
The Lynx needs to have a cart inserted for it to power up.
It also needs power. Either batteries (6 AA cells) or a PSU providing between 6V..9V of DC current up to 1A. It should boot with about 0.6A. Plus on the tip, minus on the barrel.
Stuck Batteries Problem
Old Lynx I units may have old batteries stuck in the battery compartment. Usually the last two batteries are stuck and the user believes that the unit is broken because he tries to replace the 4 batteries that come out, but the 2 remaining batteries are completely dead and prevent the unit from operating.
Bent Cart Pin Problem
Some homebrew carts may have a sharp edge that catches a pin and folds it into the cart connection. After this the cart connection no longer works. The way to fix this is to use some kind of dentists tool - a long tool with a small needle on the end. It should be strong enough that you can bend the pin back into the correct shape. In order to prevent this from happening again you could use fine sanding paper and fix your homebrew carts to have a proper slope that won't catch the individual pins when inserting the cart.
Silent Or Distorted Speaker Problem
Many power supplies have several differently shaped connectors so it may be possible that someone has pushed 1A of current directly to the headphone socket instead of the power socket. This fries the speaker. You really need to get a new speaker from ebay to fix this problem.
Broken Power Connector Problem
There is a lot of physical stress on the power supply connector in the Lynx. Very often the pins are broken and you need to replace the connector. Luckily Console5 sells replacement sockets in bags of 5.
Scrambled Graphics Problem
If the game works but the graphics is turning bad then the Suzy is the chip gone bad. Finding a new Suzy chip is pretty expensive. Best Electronics is your best bet for a replacement Suzy.
Unit not starting
Frequent causes for problems in Lynx are the aging components. The easiest way is to buy the power supply replacement and the capacitor replacement packs from console 5. This contains transistors, a zener, a MOSFET, a resistor to boost the 5V voltage and all the electrolytic caps that have dried up during the 30+ years since the unit was manufactored. Changing all these takes a few hours but with a little luck that is all you need to do.
The second test worth doing is to connect +5V from a lab-supply to the pins of the largest cap 470uF. If the Lynx does not start up now you have a more serious problem.