Problems with Dell Inspirin 17R SE (7720)

I purchased this laptop six months ago and I am pretty pleased with the value, but I have had some problems with it.

My biggest problem seems to have something to do with the power supply. About 8/10 startups, the laptop starts up, passes bios and the windows loading icon, and then diverts to a black screen for 2-3 minutes before showing me the logon screen. This is especially annoying when I don't have my charger with me, because every time this happens, the laptop crashes instantly and turns off. When the laptop does not start up properly on battery, it will NOT turn on unless I connect it to the charger and then the 2-3 minute black screen happens.

This has been a huge issue because I bring it to school regularly, and there isn't always a power outlet close enough in the lecture hall.

I have been trying to detect a pattern in it, as sometimes I do get the extremely quick start up times I should be getting with the 32GB cache drive and the problem does not always happen.

I seem to get a normal start up more often, but not always, when the laptop is fully charged and then disconnected from the wall.

My second issue has to do with the screen. Once again, randomly, the screen will behave erratically and flip through a weird pattern of colours very quickly, like an out-of-tune tube television. Sometimes the screen just gets over layed with a baby-blue colour. In both of these scenarios, the laptop is totally unresponsive and I have to hold down the power button to shut it down. My best guess is that this is due to the light wear and tear the laptop has to endure in my bag from class to class.

And finally, something I directly caused. One of the USB ports on the right side of my laptop has been pushed into the frame little so that I can't fit any USB device into it. I know that I caused it when I left the receiver for the mouse plugged in and put it in my bag, mouse-receiver-side-down.

If the latter two problems are in fact due to wear and tear (the third one IS) will dell be able to repair it? I expect that they will fix the first one if I can't find a solution here.