Is phone line working? - If not, then a phone provider issue.

Swap filter - always a good first step

Are all lights green? - If not details of the lights will help.

Make sure there are no other phones connected anywhere in the house while testing.

"dsl and internet lights are not showing"

When the DSL LED is off then that means the router's not receiving a broadband signal so the first thing to check is that the router is connected to the phone line.

Only when the DSL LED is on and steady will the Internet one come on.

I would not buy a new router in the information that you have so far. I think that it may well be the line. Not sue with AOL who is responsible for that.

I am with TalkTalk via a BT line, Talktalk did a line test with no need for a visit and no charge. I would ask AOL if they can do the same, if there is a line fault then it will be BT that repairs it also at no charge. This is to the best of my knowledge but I am not certain.

£50 visit they will only check internal wiring.

To eliminate or find out if it is internal wiring extensions etc. She needs to plug the router into the TEST SOCKET behind the front plate on BT master socket (unscrew the lower half of Master socket to get access to the test socket). Here's a picture Test Socket

If still no Internet then the fault is outside and BT can arrange a line test (no charge for that).