I am not currently aware of any computer shop capable of repairing faulty pixels in a monitor. I've been building and repairing computers for close to 20 years and I can't do it either. It's a lot easier to just replace the defective monitor. But don't let that sway you, ask around, you never know.
As for the cause, there are many. Normal use, faulty manufature of the device, poor materials, the list goes on. My advice is to contact the seller you got it from and let Ebay know as well. If you're lucky, the seller is a stand up guy and will help you out. Worse case scenario, you get a check from Ebay for the faulty device and Ebay goes after him. What ever happens, good luck and keep us posted.