LED Tape Lights Strobing
Dead power supply

LEDs pretty much don't fail.  Power supplies are the achilles' heel of LED lighting, and the primary reason why LEDs fail at all. (#2 being the lead-free [bad idea] solder crystallizing over some number of decades).  Unfortunately people cannot resist making [read: buying] cheap power supplies. 

You'll need to find this power supply unit, identify its voltage and current output, and get another one with SAME voltage and SAME OR GREATER current output.  

If you want a hand with that, get a phone camera with a flash, and shoot a pic of the label on the thing.  Then you can edit your question to add the photo.