The plug doesn't go in easily? If anything, most people here believe it to be too loose. Tablet PCs should not use standard barrel DC plugs, but instead some kind of locking mechanism and perhaps a thinner cord that doesn't impede tablet use in any orientation.

You might want to take a really good look at the plug itself, and the socket. Is there any chance that something could have gotten jammed into the plug or the laptop socket? Do you ever remember having an orange light on the laptop indicating that the battery was charging?

If something really is broken, the odds are that it is the power converter inside the laptop. I had one of those die a few years ago (in a different laptop, obviously). I was curious so I opened the laptop and troubleshooted the power board until I found a tiny blown SMD fuse. I could have replaced or jumpered the fuse, but decided to let warranty replace it with a whole new power converter board. In my case the laptop would still run when plugged in, but would not charge the battery. The good news is that if you have to send it in for service, it should be a very quick operation to replace the power board. They won't waste a lot of time trying to troubleshoot it like they would with a more expensive motherboard.

Of course it still could be the power brick. Do you have, or know anyone who has, a multimeter? There should be 19 volts coming out of the brick, I believe.