Screen is blank?
Do you mean you won't see anything at all like the signup colorful screen that says "ARCHOS Entertaining your way" ?

If your battery is full charged (did  the CHG LED green light blink when it finished charging?), and you have a blank screen, do you have a serious problem indeed. If your unit is under warranty your best and only way is contact Archos.

If when you turn it on, it takes you to the Recovery screen (white screen, usually says Code 101) then try to Format the HDD, download the latest firmware from www.archos.com for your unit, copy it from your PC to the Archos, let it finish the process wth the power supply connected, and once it's done the unit should be back working fine with the latest fimware.

But if you definetely do not see anything but a blank screen when you turn it off, your problem is more serious than a simple firmware upgrade, and you need to contact Archos tech support.