my menu button acting like it being pressed all time iPhone

Have you tried resetting your device by pressing and holding the Home (what you're calling the Menu button) button and power button until the silver apple appears?

First I'd try a hard reset of the phone.  Hold down the home button and the sleep/wake/power button on the top of the phone for about 15-20 seconds.  When you see the Apple logo pop up on the screen, release both buttons.  If this doesn't resolve it, back up info and do an iTunes restore.

Yep.  I tried that a few times and it is still acting the same way.  I also re-synced it to see if that would help, and it did not.

I haven't done an iTunes restore because it seems like a hardware problem as opposed to a software problem.  I might need to try that though if all else fails....

Try a restore but you're probably right. I'd make an appointment at the Genius Bar.