Sounds like the phone will need to be repaired. You said you purchased it from eBay.. are you the original owner, or did you buy it used? If you bought it used, you're stuck with it because the warranty only covers the original owner.

 

I hope you get it worked out! That has to be very frustrating.

 

Now that your rooted you must never use the factory reset in the privacy menu on the phone as it can cause serious problems(including bricking your phone). You can only use the "wipe data/factory reset option in the custom recovery that you should have installed now that your rooted.
Have you made a backup of your system in the recovery's "backup and restore" option(this is called a "nandroid backup")?This must be done

Did you start to experience this problem before or after you rooted and installed a custom ROM?

Sometimes the problem is in a corrupt download. Other times it is because all these things were not done when installing a new ROM:
1.wipe cache partition.
2.wipe dalvik cache(advanced section)
3.wipe data/factory reset.Now that your rooted YOU MUST NEVER USE THE FACTORY RESET IN THE PRIVACY MENU ON THE PHONE
4.format boot,system,data,and cache
5.go to install zip from sd card
6.go to select zip from sd card,chose the ROM first. It will go thru the install procedure. When done go back to step 6. and select the gapps.
When all this is done select reboot system now.

It will take 5-10min. for the initial reboot. You will be asked to sign in,skip this.

Now you can go to the market app and click on it and sign in to your google account(you must have your e-mail address and log in code).Reboot the phone twice then set up your apps. Once you get everything set up just the way you like it and all your apps are just where you want them,go back into your recovery and make a backup of that ROM. You can now delete the first backup if you need to (you might keep it if you ever need to revert back to stock to sell the phone).

If you want to install a theme it is always better to wait until you have rebooted your new ROM a couple of times first,then all you have to do is go into the recovery and wipe cache partition and dalvik cache,then do the same thing you did to install the ROM(theme must remain zipped)
When you need to install an update to an installed ROM,all you have to do is wipe cache,and dalvik.

Now that your rooted you will have to unroot and return the phone back to stock ROM and recovery before returning if that's the only option left.