You can't go wrong with Apple as they make a quality product that is extremely intuitive and great for people who aren't exactly tech savvy, but on the other hand you'll end up paying significantly more for an Apple laptop as opposed to a Windows based laptop of comparable specs.
If you ever find yourself calling the manufacture for technical support, then you'll want to stick to the big names like Apple, Dell and IBM. A lot of the other companies like HP, Acer and Sony have an alright product but their technical support departments are much more aggravating to deal with than the three I listed above.
You mentioned that your laptop is falling apart so I would strongly suggest getting an extended warranty from whichever company you end up going with. Apple has the AppleCare plans and Dell has a whole bunch of options, including ones that cover damage from dropping the laptop or spilling liquids on it. A lot of people think extended warranties are a total rip off, but after having several Dell laptops replaced and/or repaired for free I would beg to differ. =)
Another thing worth noting is that if you do go with an Apple laptop, make sure all of the software you use is compatible. Not all applications for Windows have an Apple counterpart, so you might end up stuck without a program or two... although most of the big name software companies develop for both operating systems so you'll likely be fine.
Educational Discounts @ Apple: Apple Education Store - Find Your School and Shop - Apple Store (U.S.)