It's either the power adapter or the power socket.
Easy test, try another power adapter (we have them in, easy enough just to plug one in and try it). If that solves the problem, you have a crack in the power lead, replace and it's done.
If it still has the problem then it's probably the power socket on the board (or fly lead depending on make/model). Replace this (yes we can do it) and that should sort the problem out and let you breathe again