There won't be any notification after a reboot.

Do the following:
1. In your Applications, run "Update"
2. The "eDGe Update Service" popop will check for an update and indicate if there is one. If there is one, press "Ok" (it actually will start downloading anyway).
3. Observe that at the top left corner of the LCD side you will see a small icon. It will either be animated, or will have a red number superimposed.
4. Give the eDGe 10 minutes to download. When it's done, the notification icon will no longer be animated, and simply be an upside down "T" shaped icon indicating that something has been downloaded
5. Press the "menu" button, then "Notifications".
6. At the top of the list you should see something like "A system update is ready to install"
7. Press the notification to proceed with the install
8. The installer will display a popup regarding ensuring you're on AC, and confirming to proceed. Go ahead and proceed.
9. The eDGe will almost immediately reboot
10. You will now see slightly different boot screens as the update is installed, including a special animated screen that shows the outline of a partially opened eDGe with a colour animated ribbon running through it
11. Once the update is ready, you'll be at the normal home screen.

Let me know at what point in Steps 1 through 11 your eDGe isn't doing/displaying what I've indicated. This will help me suggest things to try.