You can check the remote control easily enough with a phone camera or a digital camera:
https://www.techhive.com/article/2090126/use-your-smartphone-to-check-your-remote-control-batteries.html
If the remote has failed you may be able to find a new one on EBay, Amazon, etc.
Searched Goooge for "LCD4202 red light blinking" (which YOU could have done) but didn't come up with anything concrete. IMHO the power supply has probably given up the ghost but whether its worth shelling out to get repaired, thats up to you.
\ds;lvmS\, January 2018