Macbook crashes at startup after process bar appears Today the Macbook pro I purchased in December got quite slow, and so I decided to reboot it. I restarted it normally through the system, but it had not started up when I checked few minutes later. When I try to turn it on it seems normal first, but after couple of seconds a process bar appears, loads around one fifth through, after which the computer shuts down again. 

My laptop runs Lion, and this isn't the first time it's acting up. My hard drive crashed few months back, but IT at my school was able to fix it (has not made the "dying hard drive" clicks much since then) 

Where could the problem be, any way to fix it myself or should I bring it to Apple care?
If your hard drive was clicking audibly, I'd say the actual hard drive has failed. Even if it did stop doing it as often, that's basically the Death Rattle as far as hard drives go.
The below is a copy-paste of an answer for how to get a Macbook booting again through a really base-level disk repair, but it doesn't always work. Give it a shot, but I really recommend you call up AppleCare or go to your nearest Apple Store or Apple Authorised Repairer to organise service and have the hard drive and hard drive cable replaced.
I've modified the following a little bit from the source, since it was referring to a few things not relevant here.
Ultimately, I just hope you already have a backup.

Try a filesystem check from Single-User Mode
Start up the Mac while holding option, and then select your Macintosh HD, and before pressing the return key, press and hold the Command key and the S key. while holding them, press return, and once the screen goes black and text appears, let of of the Command and S keys.
When it finishes loading, you'll get a section of text as follows:
Singleuser boot -- fsck not done
Root device is read-only
If you want to make modifications to files:
    /sbin/fsck -fy
    /sbin/mount -uw /
if you wish to boot the system:
    exit
:/ root#

Some other messages may pop up after that, but once you see that on your screen, type that first sbin command:
/sbin/fsck -fy

That'll go though, check your filesystem for errors, and try to repair them, and if it does, then it will recheck, and rerepair if needed, up to three times.
Keep running that till it doesn't bring up &quot;repairing&quot; messages, or you get the EXACT same repairing messages twice in a row.
At that point, type reboot and see if it starts up. This is similar to using Recovery HD's disk utility to repair disk, but definitely has a higher success rate.
If at any point you get a:
Read: I/O error

then it means either the Hard Drive, Hard drive Cable or SATA controller is failing.
If you get up to your user account screen, when you type in your password, hold the shift key and then press the return key, and let go of the shift key when you see your desktop, so that you start up with the minimum startup applications and processes.
If you get it booting, I recommend copying all your files off to another disk, reformatting your Macintosh HD volume and Reinstalling OS X, since the FSCK single user method mostly just gets your drive to a workable state but doesn't usually prevent it from degrading in the future.

Again, if the drive has previously been making clicking sounds, get it serviced, preferably before your Warranty runs out.
If you can get a reservation at a nearby Apple Store, they may be able to get you started up from their network and you might be able to copy files from your computer to an external hard drive, so if you need to be able to do that, take an external hard drive in with you.
If you're going to a Authorised Repairer, but it isn't an Apple Store, they'll probably charge to do they same thing, but still worth it if you don't have a backup.