This one is already old but I just decided to post this just in case.
Note: This involves flashing some files in your PSP's flash0. A slight mistake may render your PSP useless! To access your PSP's flash0, go into recovery mode and go to "Advanced -> Toggle Flash 0". After that, a new removable disk drive should open up in your computer (assuming that you put a USB cable on your PSP to your PC, of course). Back up these files for safety.
Basically, this files makes you turn off, reboot, or go directly to recovery mode in your PSP without turning the power switch.
Well, once you get the file, there are two folders in it...
rbprx:
Place the two files inside this folder to flash0: \vsh\resource\nodule.
Once you put those files, exit Flash0 now and exit recovery mode.
To shut down your PSP, hold L trigger while choosing Network Update or the Location Free Player.
To reboot, simply choose Network Update or the Location Free Player
To go to recovery mode, hold R trigger while choosing Network Update or the Location Free Player.
rbprx_mod:
Same as the first one. The only difference are the button presses:
To shut down your PSP, just choose the Network Update or the Location Free Player.
To reboot, hold down L trigger while choosing the Network Update or the Location Free Player.
To go directly to Recovery mode, hold L+R triggers while choosing Network Update or the Location Free Player.
I only tried this on 3.40 OE-A and it works like a charm! However, still use it on your own risk especially if you are using a different OE or using the M33 custom firmware. A definite thanks to MaTiAz for making this one!