Cellphone keeps turning off?

My friend has an LG CU400 with at&t. Starting today, it wouldn't turn on. Finally, it did, but, it turned off after a minute or two. We tried taking the sim card out along with the battery and then putting it back in. This, however, only lengthened how long it stayed on til it shut off again. Later on today, when it was on, she closed it and saw it "turning off", but, it was actually restarting. Now, instead of turning off for good, it keeps restarting when you close it and open it. What could be the cause of this? Or how can we fix it?