If you can get your MacBook back on make sure it's completely up to date, so that there are no more updates in Software Update.
Specifically make sure your Firmware is up to date, Software Update should catch this. If Software Update doesn't show a Firmware Update, then you can try downloading this Firmware Update directly from the Apple website: http://support.apple.com/kb/DL1098 If it's already installed or doesn't apply to your system it will tell you this and prevent you from installing it.
If that fails you can try reinstalling Lion. This is not as big of a job as it sounds. Turn off the Macbook and turn it back on, as it starts hold (before you get to the white screen) the alt key, and choose to boot into the Recovery Partition.
When you reinstall Lion it will download the latest copy of Lion (this can take a while depending on your Internet Connection*), and install it without deleting your files (the equivelant of Repairing Windows), though to be on the safest side you might want to backup at least your most important files, however I have reinstalled Lion in this way quite a few times without any loss of data. The actual instalation will take about 1/2 hour.
*If your connection is too slow, then go to an Apple shop, connect to their WiFi and do the reinstall there. They have local copies of the latest Lion OSX, so the download should be very fast.
Otherwise, the best thing you can do is to take it to an Apple shop, you can just go there with the MacBook and tell them and show them whats wrong (don't worry if it suddenly starts working as you walk in the shop, they will still believe you). They will do their best to help you.
You will receive the best service if you don't go in accusing them and hassling. Also try to avoid the busiest times of day if you can.
Even if you're out of warranty, they will help you, although you may have to pay for repairs if it's extensive and not a problem with the model, but sometimes you can get them to do it for free.