Manufacturers like HP and Dell setup and configure the Operating System as they need to by adding in OEM information,logos,software etc.
They start with an answer file created with the "Windows System Image Manager" in the "Windows AIK" this allows them to do an unattended installation and add OEM information to the installation.
They then add in the software they want you to use/buy and sysprep the system. This removes UID's etc. and sets the system to boot to OOBE so you get to start the system into the windows introduction and create a user.
After it has been syspreped they use "imagex" to create a .wim of the system. This is the recommended way to clone the drive as it leave out unnecessary files making the image smaller.(Pagefile,Hibernate File, Temp Files...)
I have not looked into detail on these recovery systems that HP,Dell etc use but unless they are for some reason writing new software for it which is unlikely... They are using Diskpart and ImageX behind the scenes of the GUI they have for the End User.
So I am going to say you can restore your system by using Imagex to expand the wim to your main drive. Because they named it Base it may just be windows only and they have other images that get unpacked after the restoration.(These would contain bloatware more than likely)
What you would need to do is download and install the WAIK here then create a Windows PE ISO using the tools included adding imagex to the ISO. You could then boot off of that disk and use imagex to expand the wim file you might have to format the partition first before you expand to it.
Read here for details on how to do this... here is a video tutorial as well. You should spend some time researching this so you don't mess up your partitions.
Personally I would recommend you trying to get your hands on a re-installation disk and starting fresh without any bloatware/oem garbage.
Edit: If you accidentally destroyed the software to restore the WIM files easily i.e. the user friendly GUI. I would suggest you backup the information you have like the base.wim to another system and just use diskpart to create the 100MB system partition and the rest as the C: partition then use imagex to expand the base.wim to c:\ and bcdboot to create the boot information... this is in the guide I linked.
Just stumbled across this video it may not be up forever because its a sample for the CBT but it explains using wim files in an easy to understand format. http://www.cbtnuggets.com/series?id=650