In regards to calling Logitech to get a replacement, they usually do not keep parts in stock for products that are out of production. But you can call them and they may be able to assist you further.
A long time ago, I found a listing of all Logitech receivers that listed their frequencies and which devices they would work with. I'll look and see if I can find it again. In the mean time, can you post the model numbers of your keyboard and mouse? This information is located on the bottom and looks like this: M/N: M-RM63. That is the model number for the Cordless Mouseman. If these numbers are worn off, you can go to Logitech's support page and look through the product pictures and find one that matches.
I found 3 products that matched "Logitech Cordless Keyboard" and "Cordless Mouseman Optical".
Cordless Access Duo (White) http://www.logitech.com/en-us/support-downloads/downloads/keyboard-mice-combos/legacy-devices/3372?WT.z_sp=Model
Cordless Access Duo Optical (Black) http://www.logitech.com/en-us/support-downloads/downloads/keyboard-mice-combos/legacy-devices/3360?WT.z_sp=Model
Cordless Elite Duo (Black) http://www.logitech.com/en-us/support-downloads/downloads/keyboard-mice-combos/legacy-devices/3366?WT.z_sp=Model
Do any of these match yours?