The supplies you'll be needing:
Okay, sounds like a lot of supplies, but this is actually a very simple case mod.
Buying the Alarm Clock
I got my cheap-ass alarm clock at a local Wal-Mart. It was about $5 and even includes battery backup so whenever I attend a LAN party, I don't have to reset the time on my nifty case alarm clock. To be more specific, it was manufactured by Advance and is aptly dubbed "ELECTRIC ALARM : LED DIGITAL CLOCK".
Firstly, I chose to rip apart the cheap alarm clock. Do this carefully, though. You'll likely just need to remove a few screws to get all of its guts out. At this point, you may want to remove the buzzer of the alarm clock. It's always a little metal disc with two wires soldered on. It's safe to just snip the wires, it shouldn't harm the alarm clock. You should be left with just an LCD on a circuit board which is connected to a circuit board which is connected to another circuit board (and then perhaps your battery extension and/or your buzzer extension).
Now we want to prepare the 3.5" drive bay cover. You will probably want to make your own measurements for this because my job came out a bit sloppy, but if you absolutely require some direction, I cut off about a half inch of each side of the cover and threw away the middle portion.
The next step should be obvious. Hot glue your half-inch bay cover ends around the LCD of the alarm clock. Now you can probably insert your modified alarm clock into your computer case. However, we still have one issue to deal with.
The final portion of this case mod is to find a solution to power our new case modification. My answer was a simple one: I temporarily removed my power supply and threaded the power cord of the alarm clock between the case and the power supply and then reattached my power supply. (It makes the alarm clock's power cord run parallel to my computer's power cord.)
For a finishing touch, you may want to re-apply the plastic cover that originally went on the front of the alarm clock to your new case mod. (It likely came with a sticker on it that said 12:08 or 10:09.) The one that came with my clock fit almost perfectly.