my power or charge lights on my acer aspire 5735-4624 laptop won't work, what can i do?

It could be the mains adapter that's packed up, but before buying a new one get the laptop checked out at a laptop repair shop because it could be the laptop itself that's faulty.

Also check the plug-fuse on the mains adapter, fit a new one just to be sure.

They may also be able to test the mains adapter to see if there's any power getting to the connector pin.