You might want to post pictures, and be clearer on what doesn't work.
I've had breadboards where over time some of the slots just do not work. If I move the Teensy to a different row/column, it starts working again. I generally throw out the breadboard once I discover this.
Besides the breadboard, there is the issue of wiring. I've had wires that broke internally and they would only conduct electricity if the wire was at a certain angle. Over time, I have been removing all of the junk wires I got and replaced them with better dupont jumper wires. If you are doing your own wiring without using dupont wires, typically solid core wire works better for breadboards than stranded wires, but stranded wires work better if you need to move the cables. But you need thick enough solid core wire (22AWG) to make contact in breadboards. And wires do come out from time to time.
Also with dupont wires, I've had issues with some breadboards that had tight holes that if I inserted my own cables, sometimes it pushes the male pin out of the holder and does not make contact.
Note on most breadboards, the power rails are not interconnected. At the very least, I have to connect the ground and power wires across the two sides. But I do have some breadboards that the power rails are grouped in 6/8 elements, and you have to make sure each group is connected.
Of course to use the power rails, you do need to connect the ground and 3.3v pins to the power rails.
If you soldered the pins on, obviously you should check the solder connections, particularly for joints with tiny fractures. It you connect/disconnect a Teensy from a breadboard, it can possibly break the solder connection, depending on how much force you use. Using a lot of force can also bend some pins.
If you have connected flash memory chips, make sure you did not damage any of the electronics underneath the teensy and did not cross connect pins.
It can be tedious to check every single pin to make sure the pin on the Teensy is connected to the pin. I have a led with a resistor and I connect the power line to the breadboard column and the ground line to ground, and have the Teensy turn on/off that pin.
Without using a LED, many voltage meters have an option to make a sound if current can flow between the two pins. After I finish soldering, I go through and try to validate each pin. It is rare that I don't have to go back and touch up a solder joint. I also check for the adjacent pins to make sure I didn't connect two pins by accident.
Because it is tedious, I just wired up a prototype board that has 2 rows of 24 pin stacking headers to allow for checking either top pins or bottom. It has room for these multiple LED boards that have multiple leds to connect to each pin. I'm waiting for the led sets from Poland so I can put in the entire Teensy 4.1 and run a script to go through each of the LEDs in turn without having to move wires, etc. I had an extra row available in the prototype board, so I put 16 female headers on each side, so I can test Feather wings as well.
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I use Teensy's in costumes for lighting up LEDs, and I find I need to re-inspect the solder joints before using the Teensy again, and having to touch things up.