The basic check we get people to do is remove power cord, remove battery, plug power cord in and attempt startup. This performs a reset.
If nothing happens there is a hardware fault.
Then we try to narrow it down:
1. Check fuse in power socket - in your case you have power to the PSU so it isn't that.
2. Any obvious damage to power socket on the laptop? Missing or loose pin. Loose socket casing.
3. Plug in battery and try powering from that only.
If there is obvious damage to the laptop socket, we take it in for repair. Ditto if it won't power from a battery we know has charge after a reset.
If there is any uncertainty over laptop AND psu or laptop OR psu, we take in both.
I've had a couple of cases where the psu light goes out (or flickers) and we always take the psu in for that and usually the laptop as well - even if it is working on battery - just to make sure it gets fixed first time around.
Is it under warranty?
From what you described, it could be that the socket has come away from the board (i.e. by straining the cable) or that the connection became intermittent and it has arced/sparked, causing MOBO damage.