This symptom (blank screen with cursor at the top left side of the screen) in most of the cases indicates Hard Drive issues. I can try assisting you with troubleshooting. Please try the below mentioned steps and check if this helps:
1. Power off the computer and disconnect all the power sources and external devices.
2. Press and hold the power button for 10-15 seconds and then release.
3. Put the AC adapter and battery back and power on the computer and check if the computer boots normally.
4. If the computer doesn't boot normally in step 3, check in the BIOS if the Hard Drive is detected (enter BIOS by pressing the Esc key during startup and then check in "System Configuration Menu" if Hard Drive is available for boot).
5. If the Hard Drive is not listed in BIOS, Load the BIOS Defaults by pressing the F10 key and then restart the computer.
6. If you again get the same screen, take a technician's help to reseat the Hard Drive (if you wish to do it yourself you can refer to Page Number 44 of service manual).
You can download the Service Manual from Here:
Note: Before you start working with insides of the computer, please go through the "Preliminary replacement requirements" section of the Service Manual on page number 33 onwards.
7. After reseating if the Hard Drive is not detected again, you need to replace the Hard Drive.
8. If the Hard Drive is listed in Step 2, run the Diagnostics on the Hard Drive. To run the diagnostics on the Hard Drive go to "Diagnostics Menu" in the BIOS and run the "Hard Disk Self Test".
9. If the Hard Drive Test gives any error please contact HP/Compaq support for further course of action.
Do reply with results.