The way you reinstalled was a great idea. Now you know exactly what was and what was not done.
If HP has Windows 7 drivers for your laptop then you want to install those as first priority.
If HP does not have a Windows 7 driver, then you can try the Windows Update ones.
If there is no Windows 7 driver from either, then go back to HP and install an XP or Vista driver in "Compatibility Mode".
Those "Base System Devices" are components of the laptop that are not identified by Windows 7 that have no drivers and are non functional. You need to find out what they are and find and install the Windows 7 drivers for them.
The easiest way to do this is to open Device Manager > Expand (left arrow) on the unknown device to see any sub-devices > right click on the device > choose: properties > go to the Details Tab > in the Properties drop down box choose "Hardware IDs"
You will see a list of alpha-numeric names. The first one will be something like this: PCI\VEN_xxx&DEV_xxx .....
Take the PCI\VENxxx number and google it. This will give you a manufacturer. That may be all you need to figure out what the device is. If you google the DEVxxx number you might even get the device name.
Even better go here: www.pcidatabase.com
Hope that helps