It's simple to detect a [u]switch closure[/u]* and not much harder to time it if you can time it in [u]milliseconds[/u]. If you want to "get fancy" or if your program has to lots of other things and it can't constantly monitor the switch, you can use interrupts to "catch" the timing.
Of course, you'll need a "special" Arduino with a network connection. or an Ethernet, Wi-Fi, or GSM shield.
It should be feasible to send email but I don't know enough about the email protocol, so for me that would be the hardest part of this project. Maybe there's a library for that, but I don't know.
- I generally use the Arduino's built-in pull-up resistors rather than an external pull-down like the digital read example.