HELP! BSOD and essay due wednesday!

Hey, I have a gateway laptop, bought it in January, and I have had problems with the BDOD a few times, each time I just did something small and it fixed it but I made this account because I am desperate. I'm going to give as much information as possible, I hope its the right stuff.
Gateway model NV44
theres three major problems I am having, the BSOD being the worst.

1. Every time I start my computer a black screen comes up saying that There is an error on file system c: type of file NTFS label OS, it says I need to do a disk check and that the disk check will proceed in _ seconds, if I let it run through to the disk check it says that it cannot open volume for direct access, auto check cannot run due to a recently installed software package and that I need to do a system restore, then it freezes--when I try to do a system restore it says that it cannot peform the disk check and that I can schedule one for the next time my computer starts and the cycle continues. What is this? is this linked to my BDOD?

2. Every time I start my computer an error message comes up, titled "apple sync notifier" and it says "this program cannot start because CoreFoundation.dll is missing from your computer- try reinstalling this program to fix this problem- what is this? could this be connected to my BSOD?

Both of these have been happening for about 2 1/2 weeks maybe more and I have been brushing them off because they didn't seem that serious. The BSOD started today, and I cannot remember recently installing hardware or sotfware.

3. the BDOD
-titled "system_service_exception
-"check to make sure any new hardware or software is properly installed- download any updates
-if problem continues disable or remove any new hardware or software
-disable BIOS memory options such as catching or shadowing
-Restart and hit f8 to enter safemode
-***STOP: OXOOOOOO3B (OXOOOOOOOCOOOO1D, DXFFFFF88000000000, OXFFFFF88006A65160, OXOOOOOOOOOOOOOO)

Then when I restart my computer (in safe mode willnot work in regualr mode without getting a BSOD) it says "windows has recovered from an unexpected shutdown- windows can check online for a soultiontothe problem the next time you go on)

problem details -

problem event name- BlueScreen
OS version- 6.1.7600.2.0.0.768.3
Local ID: 4105

Additonal information about problem
BCCode: 3b
BCP1:0000000C000001D
BCP2: FFFFF88000000000
BCP3: FFFFFF8800F6A65160
BCP4: 000000000000000
OS Version: 6_1_7600
Service Pack 0_0
Product 768_1

Does anyone have any idea what all this means and what I should do to fix this!? it has me completely stumped, and I have an essay due wednesday. Also, is there anything I could buy like an optimizer or something that would fix tis problem? I downloaded a free trial ofone and it worked before,or an anti virus I could buy? I only have AVG free.

Thank you SO much, and I am not the best with computers so details would be much appreciated. Thanks again

Here is more info on that bugcheck code ( Bug Check 0x3B: SYSTEM_SERVICE_EXCEPTION ).

And get rid of free AVG - it's pretty useless. uninstall it with ( AVG Antivirus and Security Software - Tools download ) and install ( http://www.microsoft.com/security_essentials/ ). MSE is not the ultimate, but it is 10 times better than free AVG and it is also free.

now it is happening every time i turn my computer on, i can't do anything i triedthe stuff from the above post what do i do? i am on a different computer on these forums. this is honestly brutal

This could be a virus. I would try to run an AV scan in safe mode. Use SAS, download it to a USB stick on the other computer and run it from the stick.

honestly i feel so dumb because i do not know how to do that. i jut turned my computer on and it started some random weird thing where it says recogiering orphaned file then file names in white font with a black background so im letting that run through to see what it is

well it just randomly completed the disk check that has been freezing for three weeks, no idea why... i re started in normal mode and it bsod but then i re started in safe mode and i am doing a system restore hopefully this works. then i am looking to likely buy an anti virus or something. what should i purchuse for this? or some type of computer optimizer... any suggestions?

That's a pretty serious problem. It means your disk is mucked up - most likely the MFT. Let's hope the system can fix it. You could also run chkdsk /F to try to fix it.

PS, just saw your second post. I suggest to use MSE for the time being (see link in my post above). It is free and not too bad. But if you want top shelf (for $$), get Norton Internet Security (NIS2010). But first do a proper uninstall of AVG as I linked above too.
But even a lot more important than the AV program is frequent imaging to an external disk. I recommend Macrium and you can have a look at my tutorial. Macrium is simple, efficient and it always works - that is not neccessarily the case with Windows system restore as you may experience yourself. And the Windows7 imaging is very complex and you have to jump thru 9 hoops to do anything useful.
Get a big external disk (640GB minimum) and do daily images. Then you are able to recover at any point in time.
And stay away from "Computer Optimizers". They just get you into more trouble.

system restore won't work and now its BSOD in safe mode too

As I suspected. And if you have no images, it's back to square one.