Sounds also a bit like a hard drive problem. The clink might be the hard drive stopping unexpectedly, maybe due to a connection problem with the drive to the motherboard. If I disconnect the power to one of the drives in my desktop it makes kind of a clink-ish sound. That's all I can think of. You might want to try re-seating the hard drive, or try one from another laptop if you have one, just to see if that is the problem.
I consider this more of a feature rather than a problem. For instance, I received a Dell Studio 15 from a friend that would not power on with the power button, seeing as the cord was internally ripped. It did however, boot with the media button once the battery was charged. Usually it was a combination of the network button and media button however. Anyway, I'm not sure what started the media button power on, but if the power button does not power it on all I can think of is that the laptop recognizes the power button is malfunctioning and somehow allows you to power on with the media button. I also know there is no setting in the BIOS that turns this on, so I also find it a little strange. You might want to try contacting Dell Support to see if they have a solution. Best of luck, if you find out what the issue is, please let us know!
Parts-People.com is a great resource for finding/buying Dell laptop parts and they also have guides on how to fix it yourself. You're going to need one of the two fan models on the page below. Check which one is already in your system and then purchase the appropriate one. http://www.parts-people.com/index.php?action=category&id=... Then use this guide on how to replace it. http://blog.parts-people.com/2011/04/13/dell-studio-1535-1536-1537-cpu-and-heatsink-fan-removal-and-installation/ Hope that helps!
For the screen itself, there are different qualities of screens, and they cost different prices. I usually use Parts-People, they exclusively sell Dell parts, at a lower price than Dell will give it to you for. Here's a list of Dell Studio 15 screens from Parts-People. If you take it to a shop, expect to pay a few hundred bucks for the part and labor. Replacing it yourself would be the best bet for price. Parts-People also has guides on how to fix it yourself, the guide for replacing the screen is here. It may look tough, and probably is, but if you're on a budget it's probably worth it.