Sounds like a power supply problem.
1: Replace the power adapter with one equivalent to the original to eliminate a bad adapter.
2: Open the adapter to see if you have swollen capacitors (cap) , if so replace it or them.
3: Open the router carefully and make sure you don't have swollen caps. If so, replace them. You can tell a swollen or bad cap by looking at the top of them. It should be flat. If the tops are round or bubbled , place them. Also look for burnt or deformed components and place them .
Let me know if that helps to narrow down the problem . And let me know if the problem still exists .