My eee pc has black screen with blinking cursor in top left corner...

Hello.

Either you have an operating system problem or memory issue.

First, boot your system to Safe Mode (press F8 repeatedly when powering on). Go to System Restore and choose a date when your system worked OK. Note: with System Restore, all your updates will roll back to that date. Follow the process.

If still a problem, disconnect all cables. Be certain to dispel static electricity by touching metal. Remove the battery and memory cover. Try reseating (removing and reinserting) your memory (try one module at a time to test).

It's also possible that your Master Boot Record is corrupted. To fix, use your Windows system disk:

1. When prompted, boot from the CD drive by pressing any key. If Windows loads automatically, you will first have to enter the BIOS setup and change the order of the boot devices to start with the CD drive.
2. Once the setup loads, you will see the option to press R to repair a Windows installation.
3. Once the Recovery Console loads up, you will have to type in a number that corresponds to your Windows installation. This is normally just 1. Press Enter and then type in the Administrator password (no password, just hit Enter, unless you changed the password).
4. Now at the prompt, type in fixmbr. Your damaged MBR will now be replaced with a new master boot record and your computer should now be able to boot properly. Also run the fixboot command to repair the boot sector with a new one.

If still a problem, the last choices are Factory Restore and reinstall. Accessing Factory Restore (restores to the factory settings and will wipe out anything that you have installed or saved on your PC), is dependent on your hardware manufacturer. Boot your system and press F10, F11, Alt+F10, or Ctrl+F11 to access Factory Restore. Follow the prompts.

If still not resolved, you'll probably need to reinstall your operating system.

Hope this helps.