Most HP notebooks actually have 4 partitions, one or more may be hidden. Use disk management to see all the partitions on the drive.
HP has a way to recover Windows 7, you can make HP recovery discs or a recovery flash drive. See note below before you make the HP recovery media, You only get to make one set of DVD's or one flash drive, so use good quality DVD+R media or good quality flash drive.
These HP recovery discs will return the PC to as shipped condition no matter what was done to partitions and you should make these discs just in case the other Windows 7 image does not work out. Just a note about the HP Recovery Software, it will wipe all your data but will give you an opportunity to back up personal data and settings before you actually start the recovery process.
Note* I also suggest you run the HP Support Assistant while in Windows 7 to install all the latest updates for your PC, it can be found in the HP folder in the All Programs start menu, once it loads, click the Maintenance icon, then when it loads, click the "Refresh" icon, install any updates it finds. This is important to do before you make your HP recovery media, this way they will contain the latest HP recovery software.
HP_TOOLS partition is important, it contains diagnostic tools for your hardware, the bios updates will also use this partition to store a backup of your old bios in case the bios flash does not work, so you can recover from a failed bios flash.
To answer your question about the Windows 7 System image you made, if you included all 4 partitions when you made the image, it will restore the PC to just like it was when you made the image. Unfortunately W7 image software has no ability to verify the image it made is actually a good image, I prefer EaseUS Todo Backup for backup images, it is much more flexible and Free.