Phone Trouble

My phone is pathetically slow, has an annoying ringtone, and loses its charge in about three hours, seemingly at random, but I have stuck with it because it's a flip phone (which is neato) and came free with the service I inherited from my sister. It's started pulling something on me, though, which I cannot let pass, of just BEEPING for NO APPARENT REASON. I've checked the voicemail, the text messages, it's charged, it's got enough money for the next month which isn't coming due for a while anyway, I've unset and reset the alarm, then turned the whole thing off and back on again, but nothing is good enough – WHAT DO I DO??

Or better yet, I should get a new phone and drop-kick this one into an environmentally sound receptacle. Any suggestions? My only requirements are that the buttons respond within half a second of pressing them (preferably instantly, but let's not get overambitious) and that I can load my own ringtone (or is that a service provider thing?). It would also be nice if it gave me the option of sending a text message to an email rather than a phone number. Help!

EDIT: Thanks to Rupertistheone I devised a cunning plan of pretending to swap the battery (merely taking the battery out for thirty seconds or so then putting it back in) which seems to have done the trick. Dumb phone, hahaha. Thanks for all the advice!