Laptop Screen Not Working, Audio Buzzing?

I have been using for a while a Toshiba Satellite c650 laptop. It has been used only to listen to music and to check e-mail via Internet Explorer. Recently, after a short camping trip where rain was abundant, the screen stopped functioning. The computer was working, we could hear the music playing. After shutting it down, turning it back on would make the screen work for anything from a few seconds to a few minutes. The screen then remained pitch black, whatever we did. I finally had the idea to plug in my 27-inch external monitor.The results weren't as good as I expected. The external screen works fine, but the resolution cannot be set higher than 1366x768, instead of the usual 1600x900 on the laptop. Also, when connected to my Alienware laptop, the external monitor can go up to 1980x1080.As if this wasn't enough, when playing music, the speakers would suddenly let out a very loud buzzing noise for a few seconds. We have tried to pinpoint the cause, but it happens whenever it seems to want to.

Is there anything we can do about the screen? (without sending it to be repaired, of course) I guess there's a problem in the hardware, because the external screen works. There might also be a problem with the video card, because of the weird maximal resolution..