Restoring factory setting

Your phone has been jailbroken, and we can not help you here. Sorry

Apple won't even look at your phone since it's jailbroken. Ask the jailbreaking comminity for help in getting your phone working 😉

No you will have to buy a new phone.

Go into computer>C drive> App data (could be in documents and settings >owner if you are using xp or in your user folder if you are using vista or 7, you also will need to make sure you have show all hidden files and folders checked in folder options) > Apple Computer> iTunes> iPhone software updates> and delete and downloads you have

Now put your phone into regular recovery mode (not DFU)>> while the phone is powered off hold down the home button, plug it into the USB cord, and release it only when you see the iTunes logo

Now restore and update your phone, iTunes will download a new software update for you since you have deleted it..should be good from there.. it worked for me

Jailbreaking doesn't void your warranty. It only voids it if the jailbreaking itself messed up the phone.

Wrong.

I do know 100 percent from personal experience that I am not wrong.

In addition, read this article

http://support.apple.com/kb/HT3743

Please note in the very last line the word "May"

May is a month of the year! Try it and see if you get if fixed or replaced under warranty since your 100%.