its just something to try but i have no guarantee it will work. running the battery down will not lose any data.
press and hold the power button down for 30 seconds or so. try the power button plus UP volume for greater than 30 seconds.
this is a pickle of an issue to try and resolve over the internet as its hard to ascertain what your phone was doing, what app was running at the time of this issue--could be a faulty app or any number of things. this is why factory resets were invented.
other than those options, im not sure what else you can do short of a factory reset.