I believe there is a problem if the phone is playing music with BoomSound on and then a call comes in, it can screw with the earpiece settings. Try turning off BoomSound and then reboot the phone.
I can vouch for this heating method. I purchased a 4S with greyed out wifi, and n/a for the wifi address under the settings. The bluetooth was showing an address under settings but would continuously be initialising itself. I removed the back, battery and EMP shield as per the instructions above, and warmed the wifi chip with the tip of my soldering iron for a couple of minutes (I don't have a hair dryer). I re-assembled the phone, turned it on and BAM....the bluetooth was on straight away. I went into wifi, which was now no longer greyed out, selected my router and connected. I can turn the wifi and bluetooth on and off and they connect successfully every time. 100% perfect result!
I have exactly the same issue. Iphone 4 wont turn on unless connected to PC, and continually goes through a boot loop. I'm guessing a bad battery. However, I went one step further. I have one of those battery pack cases, so I put my phone in that. It turns on fine and boots up ok, but itunes will not see it. Shortly after I plug in the USB cable, it reboots and goes back into the boot loop. If, however, I put it into recovery or DFU modes, then itunes sees it ok. Restoring brings up an error 1394 every time. I'll replace the battery and see what happens.
You still need to remove the back of the phone to disconnect the digitizer connector. Then you need to heat around the perimeter of the screen to soften the tape and separate the digitizer from the LCD. Stick the new one in place and run the connector through to the main board. Replace the back. Good luck not cracking the LCD :)