What is your computer operating system, and is it 32 or 64 bit?
At this time, is Premiere Elements 12 listed in Control Panel/Programs as an installation product?
Where did you purchase this Photoshop Elements 12/Premiere Elements 12 bundle - from Adobe as an online download or from an authorized reseller offering the box packing with installation discs? From your "The download doesn't seemed to have worked", I am assuming that this was an online download from Adobe.
On your computer, you should have started with 4 installation files
Photoshop Elements 12. An .exe file and .7z file specific for Photoshop Elements 12...and file targeted appropriately for 32 or 64 bit computer.
Premiere Elements 12. An .exe file and .7z file specific for Premiere Elements 12...and file targeted appropriately for 32 or 64 bit computer.
You double click the .exe first and afterward as indicated .7z.
Each of these products will have its own serial number.
Do you now have those components. If not, then you need to start again with the download to get those files on your computer in order to start the product installation.
Please review and consider. Any questions or need further clarification, please do not hesitate to ask.