Half the screen is grey?!

That's a hardware fault. Apple does not repair those, they replace the entire phone. The OOW replacement cost for an iPhone 4 is $149.

Apple does not sell iPhone parts. There are no legitimate sources for iPhone parts. Attempting to repair it yourself will result in forfeiting your ability to ever get it serviced/replaced by Apple.

You might be able to get it fixed cheaper at a third party cell phone repair shop, since your phone is already out of warranty. Definitely cheaper than $149, if they can fix it. Worth a shot!

Just be warned... If they open it up and can't fix it, Apple will no longer touch it.

True, but it's going to cost a lot more than $149 to replace it if it's been opened by an unauthorized party.