Copy disks to file then install.
Does your Lenovo have a USB 2.0, or 3.0, or a FireWire port?
If so, then I see two methods, but they will involve other equipment, at some point:
Curt's suggestion should work just fine. However, you will need a computer WITH a multi-drive (either internal, or external). With that other computer (maybe even one on display in a computer/electronics store, or at a friend's house), just Copy the full installation disc(s) to a USB thumbdrive, and insert that into the USB port on the Lenovo.
Borrow, or buy, an external USB 2.0, or 3.0, or FireWire multi-drive, and use that to install from. If you borrow, I think that I would do it very slightly differently, and would Copy the installation disc(s) to my internal HDD, and install from there.
Possibility would be to download the program's installation file(s) for the trial (say from ProDesignTools - be sure to read ALL instructions carefully), install, then plug in your S/N to convert that trial to the full-paid version, and Activate. Obviously, you will need an Internet connection for this method. However, since you are posting here, it is very likely that you have an Internet connection available somewhere. This would probably be the way to go, if your Lenovo does not have USB, or FW.
Download PS from Adobe Web Site and use the Serial Number which came with your Disc.
This is the direct download link for Photoshop Elements 10 installer for Windows.
Follow the download instructions carefully or the links won't work.
Thanks for your help. My colleague saved it to a USB which I then used to upload onto my thinkpad. All up and running now!