If it is an Android, your fail-safe reboot is removing the battery. When you put it back, you should be good to go. You shouldn’t lose any of your info. But now is the time to look into using cloud-based apps to store your contacts and calendar (like Gmail).
If you are using an iPhone, the batteries are sealed. So it’s a bit trickier. First plug in the charger, wait 2-5 minutes and see if it comes alive. If that doesn’t work, hold down the Home (circle) and the power button at the same time for a FULL 30 seconds. If it comes alive, turn it off to let it reboot. Go get a glass of water (or something stronger) and come back after about 5 minutes and turn it on. Whew! That was close!