If you're connection is a "wireless" connection, I recently fixed a computer with such issues simply by installing the most recent Broadcom wireless driver at HP's site.(It fixed "Standby" and "Hibernation" issues.) Obviously, you'll need to check your Device Manager to confirm which wireless driver you are using, but it's worth a check at the HP site for updated drivers..

In addition, make sure that the ethernet driver and the chipset driver are also updated.. I've seen updated versions of both depending on the exact hardware you've got installed.

It may require a new BIOS version to fix the problem but I would perform that option last if it's needed at all.

Hope this helps.

Grif