Hello Mku,
Welcome to the HP Forums! I hope you enjoy your experience!
I understand your computer will not wake up from sleep mode sometimes. Sometimes, depending on the situation, this could be known as hybrid sleep mode. I will do my best to assist you!
As I suggested, your Windows might perform "hybrid sleep" instead of the regular sleep mode. This would illustrate the exact situation you have explained. For instructions on verifying, enabling, and disabling hybrid sleep mode, please reference this website: Turn Off Hybrid Sleep in Windows
Please note that the steps are intended for Windows 7. However, these steps are applicable on Windows Vista as well.
If this does not resolve the issue, the next troubleshooting step will be restoring the power defaults to normal settings. To perform this task, go to the start menu, type “CMD” in the search bar. Now, you should see a shortcut for CMD above. Right click on it, and click “run as administrator”. If it asks you for administrative permission, please allow permission.
You should see Command Prompt open. Type the following command in this window and hit Enter afterward (without the quotations): "powercfg -restoredefaultschemes"
If the issue still persists, the next step will be performing a hard reset on the desktop. To do this, turn off the computer, and unplug all cables attached to the tower and monitor (including all power sources) for a few minutes. Plug all the cables back in and turn on the computer, and observe the results.
if the issue is not eliminated, I would encourage you to attempt a System Restore. If the issue was caused from an update, this will allow you to return the computer to a restore point before the issue surfaced. I will provide additional information on how to do this: What is System Restore?
If the issue is not resolved, I would try reinstalling the operating system next. I suggest this because there may be a software/driver conflict. A recovery would refresh the operating system. Before you reinstall the operating system, you should back up everything first. This document will provide suggestions on how to do this: Backing Up Your Files (Windows Vista)
Once this is done, you could perform the recovery. Information on how to do this is provided here: Performing an HP System Recovery (Windows Vista)
At this point, you are likely experiencing a hardware failure if the issue is not resolved. At that point you should contact HP technical support for additional information. You can utilize this website to locate the most suitable number, based on your region: Contact HP Worldwide
I believe these steps will resolve the issue. Either way, please provide your results. Thanks for bringing this issue to the HP Forums. Have a great day!
Mario