iPhone 4 keyboard not working, Apple support

So here is the situation: I bought an iPhone 4 when they first came out last summer and that iPhone worked great for me, but a couple weeks ago the top button started sticking and wouldn't work so I sent it to Apple for "service", in actuality the service was just to send me a refurbished iPhone. At first, this iPhone was perfectly working, but then I noticed that it would randomly shut itself off at least 3 or 4 times a day. So, I sent this one back to Apple. The next one I received is the one that I currently have. It worked fine for about 20 minutes, then as I would start typing a text message, the keyboard became unresponsive and erratic. I would press the "L" and it would type a "Q", if I tap the top of the screen it opens an application at the bottom, if I type one letter it continues typing about 30 random letters. It is useless. I tried restoring it and performing hard resets. I have had iPhones since the first one so I know how to work the keyboard, this is just a defective unit again (my guess.) My question is: has anyone else had this problem with the keyboard and solved it. Also, can I call Apple without paying for tech support and nicely ask for a WORKING unit?