|The power adapter is "usually" something like a rectangular block with a cable (usually) permanently attached which plugs into the laptop. there is also another cable (usually) detachable which connects that block to the mains outlet.|
It is rare for the mains cable to fail, but not uncomon for the cable which connects to the laptop to fail.
I doubt the main power cord (which plugs into the wall outlet) is faulty, as if it was there would be no indicator lights showing on the laptop.
What I am suggesting however is that the actual adapter itself (the block) may not be providng correct volts out, or enough current, to power the laptop properly; even though it can light up the various led indicators..
Occasionally the laptop power adapter mght be built into the actual plug whch goes into the wall outlet, and thus there is just the single, thin(er) cable from that to the laptop. However unless the laptop is more like say a tablet, or the mini notebooks, the adapter is likely to as described earlier above.
This eBay link shows typical power adapters as used on many laptops, other than Apple.
As earlier, visit a local store and ask to test your laptop using one of their compatible adapters. If the problem persists even with their known good adapter then the problem is within the laptop itself.
message edited by trvlr