Blank screen often is phone not booting up, not necessarily the display.
Any internal fault can give you same problem.

Did you know that the phone and screen can be turned on and off independently of each other? The phone CAN be on and ready to use when the screen is turned off. You can use the other features of the treo without turning on the phone.
If you are not on a call and the screen is off briefly press the power button to wake up the screen. Just do this once! Repeatedly pressing this will just turn off the screen again.
Press the center of the 5-way to turn off the keyguard (which I almost never use) Then, press the power/end button and be patient to wait for the signal to show up.

It sounds like you have set your screen to turn off after 10 minutes of inactivity. If this is okay, then so be it . If not ,you can change this by going to settings>power>advanced, and select the amount of time you wish the screen to be on. I have 1 minute when on battery, and 5 minutes when on external power.
Auto-keyguard and touchscreen lockout automatically enable keyGUARD after your set period of inactivity. To disable, press center of 5-way.

I do not use keyguard because I found it to be more of a PITB than helpful. So my keyguard settings under the settings tab>personal>keyguard are:
Autokeyguard: Disabled
Disable touchscreen: unchecked (while on call in today screen)

The phone and screen can be turned on and off independently of each other? The phone can be on and ready to use when the screen is turned off. You can use the other features of the treo without turning on the phone.
If you are not on a call and the screen is off briefly press the power button to wake up the screen. Just do this once! Repeatedly pressing this will just turn off the screen again.
Press the center of the 5-way to turn off the keyguard (which I almost never use) Then, press the power/end button and be patient to wait for the signal to show up.
It sounds like you have set your screen to turn off after 10 minutes of inactivity. If this is okay, then so be it . If not ,you can change this by going to settings>power>advanced, and select the amount of time you wish the screen to be on. I have 1 minute when on battery, and 5 minutes when on external power. 
Auto-keyguard and touchscreen lockout automatically enable keyGUARD after your set period of inactivity. To disable, press center of 5-way.

(try holding down the power key when placing the battery into the unit to do a hard reset)

hope this helps

You may have a faulty screen

Have you tried a HARD RESET?

Perform the following steps:
Pull the battery out. Put the battery back in while holding the RED button down and a reset screen will appear.
Push the up button on the five-way to start the reset process.
Alternate process:
Similar to the hard-reset of the Treo 650. Remove the battery cover.
Press and hold the Red radio button.
Use the stylus to depress the reset button next to the battery.
Push the up button on the five-way when you get a prompt to "Erase all data".

Replacement screens are available on ebay.