Take a flashlight, and a dental hook...
Shine in the ds-lite cartridge slot look for a contact that might be bent different and repossition it with the dental hook.
For if your 2ds works, it can't be your ds-lite software (ds-lite doesn't update security, while 2ds does).
still it's a good idea to do the official firmware update (twilight menu will be the same, just compitablity with 3ds firmware should improve.
Firmware effects hardware and firmware compatibility of your handheld.
Kernel / wood / ysmenu / Twillight Menu++ effects your game compatibility.
Firmware updates are as far as i know limited by the manufacturer of the flashcart unless it can be flashed to work a general R4DSi, but that's mostly not possible due to HWID and unknown IC used in the flashcard.
and it's dangerous for it being flashed wrong can't be undone.