the only way to fix the crack is to replace the shell. and unless you know what you're doing, paying $50 is probably the safer and cheaper way to go.
a new case can be had for about $12-15 from dealextreme.com, however the quality or many of them, while nice, is not the same ridgidness/sturdiness as the oem cases. in addition, unless you have patience and are good at working with small electronics, my suggestion would be to simply pay the $50 rather than risk damaging something else in your system (eg. the microphone and/or wi-fi antennae wires or the flexible cable leading to the top display).
some of the people who I've helped in the past would have saved themselves and me a lot of grief had they not attempted to repair their systems themselves.
as far as a preventative measure, the things that you can do in the future are as follows:
- never open up your ds lite beyond the first click (which is almost flat). opening the system so that the face opens completely flat puts unnecessary stress on the plastic surround the axle hinge.
- always try to open the system from the center or left side of the top half [d-pad side] (not from the right (like most right-handed people tend to do), doing so slightly "tweaks" the top half and places unnecessary stress on the left side of the system where the axle hinge is.
edit:
you don't want to crazy glue it. doing so will melt the plastic, weakening it as well as potentially gluing the axle hinge (which would then cause you to snap the system in half when trying to force it open).