Sorry that you are having a problem with your printer and power issues.
See if you can unpluch it and check if the carriage moves.
Check all areas for a paper jam. Sometimes a jam can occur from a small piece of paper and locks the carriage. This could be causing the constant light blinking.
You can also perform a hard reset. Unplug the power cord from the back of the printer. Leave it out for 30 seconds and plug it back in.