Function keys failure after partial system reinstall  

I found lots of old threads about similar problems, but none helped. Odd, as one had identical machine to mine, but a different sub-problem.

Machine: Dell Notebook Inspiron 1545.
After struggling with malware-caused trouble (noted on this site in another area, and partially fixed with your esteemed help), now I ran a Dell part install DVD. It helped somewhat. But --
it also killed all the previously working function (F) keys!

The obvious solution was to get a fresh keyboard driver from Dell. But that also failed: their driver, tailored to my personal Product Key, was named 'Mouse, keyboard & Input devices'. But there was no selection. It just cheerfully installed one for the touchpad, and that was all it had. No keyboard. I installed as directed, but after reboot there was no change -- as expected.

A total reinstall may not be possible, as this machine was an immediate upgrade from Vista on the first day Win 7 came out, so I never got the Vista 'restore' DVD, only the 'upgrade from Vista to Win 7' DVD. (a situation which persists after a 20-minute phone call to Dell in Manila. Who claimed "we no longer have those Vista DVDs"!). So I am reluctant to try the pseudo-total reinstall without trying to fix this problem instead.

Any ideas, please?

Dear Maxie, I recall Quickset from a much older Dell. I got it now from the Dell site. And installed it. A slow process as it checked my machine. But then, after it noted a successful install -- I simply could not find an executable file where I expected it. Nor anywhere else on my system! Weird...

Also, the driver link to Dell that you helpfully provided led to the same place I had been, where the 'drivers and keyboard' link contained only one for the touchpad. I ran it anyway but it had no effect.

(Hi to Belfast. Have been there 3 times over the years. And recently watched the drama Titanic: Blood and Steel !)

Maxie: I followed your link. It ran ok, but reported "no integrity violations."

32 bit

Maxie: a noble effort from you. I installed the file okay, and rebooted. Function keys do return, but only 4 out of the 12, and they are Intel defaults, different from the Dell originals, so no use, really.
Time to give up I think. Also because of those various 'other problems' within programs caused by all this.
So now I will push the 'factory default' restore disk past the high-risk point. It may screw things up irretrievably. But anyway, I will then try to talk Dell out of the proper Win 7 install disk, and if not, I will bite the bullet and buy the disk (about US 120 it seems).
Again, thank you for your valiant attempts.