Since a similar thing happens after other updates, it probably is not directly related to "uninstalling google desktop." Does the same thing sometimes happen when you do a regular restart (with no update or uninstall)?
You can try doing a SMU (power management) reset. Before you do that, reset PRAM.
If that does not help, follow this procedure precisely to reset the SMU
When you reconnect the power cord, if you were using an power strip of some kind (especially if it's old or overcrowded), try connecting it directly to a wall outlet by itself (at least initially). Start it up with only the power cord connected, then (if it starts up normally), add only standard USB keyboard and mouse. Use it that way for a while to see if there's improvement. If it's better, add your other peripheral devices back, one at a time, to see if the problem returns.
You may want to run these "standard" fixes if the problem persists.
1) Check the amount of free space on your harddrive. You should have a several gigs free.
2) You should run disk utility
a) verify the disk
b) update your permissions.
3) Try a safe boot.
Shutdown your machine. Hold down the shift key. Poweron. Wait awhile Wait awhile while you harddrive
is being checked.
4) You may want to run applejack to clean up your machine.
a lot more ways to fix your Mac.