Bought used bike, Shimano derailleur does not work - how to repair or replace?
The derailleur in the picture has been scratched and the cable is connected wrong, but it should work if you install the cable correctly.

Searching for "RD-M53P SGS" does not find anything except this question. However, all Shimano rear derailleurs specified for 9 speeds and below have the same actuation ratio, so any of these should work. The derailleur in the photo looks like 9-speed model and it is installed in 7-speed bike.