First of all a sim card shouldn't be causing your phone to reboot, I am more of a PC guy so I could be wrong here (I did do a quick Google search for that and corresponding results were only of unlocked or used phones, did you buy your phone new?). Anyway you should probably try to open the phone, should be the easiest. Or you could go to a small phone repair shop, the kind where you actually talk to the technician and don't have to leave the phone there before someone even takes a look at it, they would probably get it out for free, especially if you are going to have them check out what's wrong with the phone. Hope this helps!
Do you get a beeping sound and a flashing yellow light? If so, you may be experiencing the infamous "Yellow Light of Death" (aka YLOD). There are several ways to fix this problem, however they all require you to open the console and mess with delicate components, it is possible, but only if you feel up for the job. If not, send it to a reliable repair business.