I've lost control of my iPhone's home button
My iPhone's home button has recently been activating on its own at random. Siri, multitasking, apps exiting, more screenshots than I can count, all without actually pressing the home button. Raise to Speak is off. This happens regardless of if anything is plugged in to the headphone jack, phone orientation, or if the phone is even being touched.
I've already replaced the home button, which worked for about 3 or 4 days before acting up again. Apple Store suggested a screen replacement, but I'd rather just put that money toward a new device.
The battery has also been wonky and failed Apple's diagnostic test. Obviously this needs replacing, I only mention in case it could be related.
What say you, iFixit community? Am I doomed to a screen replacement? Or is there something else at play?
Verizon iPhone 5, 16GB, iOS 7.0.4