Here are the spec for your HP G62-340US Notebook Computer. As you have noticed, the are no Windows 8 drivers provided on the HP Software and Driver Downloads page for your computer. And while your computer may be capable of running Windows 8, THIS is HP's position on Windows 8 support and any HP computer not originally supplied with Windows 8;
Not all Windows 8 features may be available on all PCs.
Your particular experience with Windows 8 will be determined by the capabilities of your PC.
HP is providing upgrade instructions and drivers will be available for most Windows 7 systems sold after 1st October 2011.
If you want to restore the original operating system after upgrading, you must create HP recovery media before you upgrade.
Please note that if you purchased your system prior to October 1, 2011, HP has not tested these PCs or developed Windows 8 upgrade instructions or drivers for them. Upgrading such systems may be difficult or impossible.
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Important information regarding additional limitations and requirements;
Screen Resolution Requirements
Limitations with DVD playback software
Limitations with Blu-ray playback software
Limitations with TV Tuner software
Secure Boot & other UEFI dependent features
Please try the following drivers;
AMD Catalyst™ Display Driver or AMD Catalyst™ Notebook Display Driver
Realtek HD Audio Driver (check "Accept", click "Next, and select download location for 2nd item down)
Realtek FE LAN Driver (select download location for 2nd item down)
Realtek USB Card Reader (select download location for 6th item down "Reader Checking Tool" and run this tool. Next, download driver per tool from same Realtek page)
Please post the Windows Device Manager "Hardware Ids" for any/all other missing drivers, including the wireless network evice on your computer.
You may also wish to update the BIOS to sp52074.exe F.27 2011-03-01, if you haven't already done so.
Please send KUDOS