Good to know we have computer geeks on board!

I'm no help here, but I DO know that you can turn that little touch pad off. I hate those things. Get a wireless mouse and call it good. I hope you get your problem sorted! Sounds like a few people here know how to help

I've seen some people tape over their finger pad with cardboard & just use a mouse .

This may work
Type 'Recovery Drive' in the search box at the bottom left. Click on the app that shows up. This should start up Recovery Media Creator.
Perhaps you can save the files that are created to a D drive partition that you created using the Disk Manager function.

Try ScienceBikers suggestion FIRST!

There should be a hotkey combination to restart you computer and restore it to factory settings. Doing this will erase all data, so be forewarned. You can try system restore as well, although I can't remember if that will actually restore a partition.

The D: drive is usually the DVD drive!! Are you sure you deleted the backup (as in factory reset, not really a backup) partition? If I am in error and you did delete there are some utilities that can restore it. Just don't attempt to save data to the drive until you 'undelete' it. (Partition Commander, etc)
All else fails, recreate a new backup partition - note that the only safe place for a true backup is on a different hard drive, flash drive, DVD, or other media - not on the same drive.

So it still works okay and boots up? It's just the backup that's toast. Not the end of the world, right?

When you get things going again, check out this mouse, it's 15$ and it's fantastic:

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Did it actually delete the D partition?

Seems you should be able to remap the drive.
The partition is still there, just not the map to it.
Do youtube or google search for map drive instructions