Resetting an unlocked and broken phone?

Hi all,

First off, I apologise if this has already been asked in the past. My forum searching skills are sub-par at best.

TL;DR:
I own an old iPhone, bitch has been crashing, **** is IMEI unlocked and jailbroken, how do reset to factory settings?

Director's Cut:
I recently got an iPhone 4 and got it IMEI unlocked. It was a second hand phone bought when iPhone 4's were first around and passed down like some kind of pretentious heirloom, but I have a problem.
Every now and then, sometimes 5 times a day, my phone will just shut down. I can see what I was doing, but it slowly fades away like when you rip the batteries out of a switched on GameBoy.

All I can think of is that I've somehow messed the phone up, and so I want to reset it to factory settings.

Problem is, it's jailbroken and IMEI unlocked, so I'm wondering if it's possible to both undo jailbreaking, and restore my phone to factory default without losing the unlock?


Thanks in advance all