Macbook screen bottom half black

In general, extended warranty plans are a healthy-sized profit center for the company offering them. This implies that unless a product turns out to be less reliable than predicted, on average (mean average) customers will be better off paying for their own repairs without the warranty. However, if one can't afford to self-insure for abnormal or even normal deviations from the average, something like AppleCare will lessen the downside financial risks.

Thus, I suggest (and buy) AppleCare only if an Apple product seems to be getting numbers of reports of below average reliability (e.g. the Duo 2xx and PowerBook 5x00 product lines). For other Apple products, maybe put the money in a savings account instead, and there is a good likelyhood that you'll end up ahead after a decade or two of Apple products.

It sounds like your backlight has broken. The LCD screen needs to be lit from behind before the screen contents are more than vaguely visible. If you boot the machine again, and shine a bright torch from the front, you should be able to see your usual screen layout for login etc, but obviously everything is going to be very very dull. If this is the case, then you can get that fixed with relative ease at various repair centres or through a slew of online guides.

Sometimes on older hardware it's not the backlight that's gone, but instead the tiny starter/transformer that is required to kick a backlight into life, although this type of method isn't used on modern LED backlit screens like your Macbook