Bob,
as was mentioned in the earlier posts in this thread, the code you need is 1005, but this code does not come pre-installed in any of the OFA or R/S remotes, it needs to be added. If you have an older R/S remote, it might be upgradeable via phone (models like 15-1918 are phone-upgradeable). Or, if you have a Producer 8 remote, these can be upgraded by mailing them in.
I'm not familiar with the 15-1935, what does it look like? Would you be willing to scan the picture off the box and email it to me? I know that Radio Shack put out a remote called 15-1934 which was a version of the Producer 8.
Rob.
[Link: stormloader.com]