So, yeah, all my buttons were working when I got home from the store today (around 730 pm). I didn't take it off the nightstand where it was until I picked it up again at 1100 pm. I typed in my password (which included using the "e" button), and it let me. I went to reply to an e-mail and noticed that it wouldn't let me type the letter "e" in a word. It was also being ridiculously slow.
Since the "e" button is required for the password to get on the phone, what can I do to fix this? No, it didn't get wet, nothing changed from point A to point B. I tried resetting it several times.
Do you have access to the phone now? If so, I would back up your info using Desktop Manager, then take it back to the store for a replacement. You can later hook up the replacement and do a restore, and all your settings and contacts will transfer to the new device.
If you don't have access, I would take it back to the store for a replacement, and find out if you have any options to transfer your info. Then someone there can help you do a factory reset, which will erase all your info. When exchanging, remember to remove your SD card so you have any photos and other files you have stored there.
You can replace your device under the Device Replacement Program.