Hey man, I know it's a little late for the advice but I had the same problem. But there is a better solution.
Here is the chain of events for everyone's future reference:
1) generally when trying to download something (an update or game, etc.) the system will appear to just hang or take forever with no visible progress (or no download indicator circles).
2) you hit cancel to back out of the download and are brought back to the home menu screen.
3) you hold down the power button and the standard "power off" button appears on screen.
4) At this point the entire system appears unresponsive, the touch screen does not respond, the screen is on but will not let you power off of tapping the the button on screen, the PS button stays lit blue.
5) pressing and holding the power button for 20 seconds or more does nothing.
6) attempting Hard Reset (holding power, PS and R) appears to do nothing.
7) and then the screen appears to turn off (as if in standby mode) but the PS button stays lit blue.
AT THIS POINT TRY TO STAY CALM AND DO THIS:
1) hold the power button, PS Button, and R bumper simultaneously for 20 seconds.
2) wait 10 seconds
3) hold the power button only for at least 20 seconds
4) You should see the PS logo appear on screen and enter the safe restart menu
5) select RESTART
6) breathe easy, your PS Vita survived.
REMEMBER: This just takes a little time. Wait for the screen to go black, and then wait a minute or two before trying this solution. All I can say is that it worked for me, I hope it works for you if you find yourself in this situation.