If I plug it into the usb cable to connect it to my computer, my computer recognizes that it is there and adds a removable disk to "my computer". But when I click on the removable disk to open it, I get the message "please insert a disk into drive G:". I know this is the correct drive because it is the only removable disk currently on my computer; when I attach my digital camera or my thumb drive, my computer reads their contents just fine.
Also, as my husband also has a touchpad, I connected his touchpad to my computer; it came up just fine, and when I told the touchpad to go into usb mode, the computer was able to read the files. However, when I told the computer to eject the drive (so the touchpad would be happy) but then didn't physically disconnect the touchpad and tried to open it from "my computer", I got the same "please insert a disk" error.
For the phones at least, this behaviour is normal. You cannot read the disk before USB mode is enabled or after you have ejected it. Read "Please insert disk" as, "Enable USB mode".
I turned off my phone with the switch, then plugged in the USB cable. This caused the screen to light up and display the lock screen, so I would be able to touch in the code and enable USB mode from there. Not having a touchpad, I don't know, but assume it would behave in the same way.
If you are unable to turn on the touchpad with the switch, then this suggests a power issue and if it doesn't turn on when first connected to the USB cable, I'd guess it might be the battery connection, but you are right that it could also be the symtom of a disconnected screen or backlight failure. You could try using / plugging in the touchpad with a strong light on the screen to look if you can see anything. You could even try switching on the unit in a dark room and look for a faint glow which might suggest the backlight works, but the screen is black/off. Of course the possibility of some catastrophic software failure remains possible. You have no doubt searched for similar threads here.
I shutdown & pulled the battery from my phone while connected to the usb cable - it remained recognised as a removable disk until I pulled the cable out and reappeared in 'My Computer' when I reconnected the cable - still with the battery removed and the screen STILL lit up with a battery symbol. Again, your device may function differently.
Hopefully someone with experience of your device can help more. I believe the battery is 'built in' - only removeable by disassembling the device, but I think it's possible to do this and there is probably a guide to doing this somewhere. You could at least inspect battery, screen and backlight connections and if you have a metering device, check the battery charge.