Or do I have to bring it to someone else's house and use their landline broadband?
That has got the best chance of success and has worked for other forum members with similar issues.
However, even if you get it activated at someone else's house. There is still a long term communication issue to resolve, the same thing that is causing your activation issue will also prevent RailMaster from invoking the 'auto' application update routine. It won't stop you from updating RailMaster, but the update will have to be downloaded manually and installed manually. That means keeping abreast of the current RailMaster version information stated at the top of the RailMaster section of this forum. Also, when RailMaster starts up, it does an Internet check and can sometimes update the 'Locomotive Database' files silently in the background. This won't work either without the Internet communication issues being fixed permanently. Again, when a new update is released that can be manually installed, the manual update will also include any of the 'Locomotive Database' silent updates that might have been missed.
So in conclusion, many users run their version of RailMaster in locations that do not have any Internet access such as outbuildings for example and rely entirely on manually installed updates or even no updates at all, if what they have working totally suits them. The current version at time of writing is version 1.73 ... we know that there are some members still running version 1.69 or even earlier and are not in the least bothered about updating.
In my experience, HRMS have always responded to my communications [in my case via the inbuilt 'Help' system] within hours. But I have also seen reports on the forum where some members have taken many days to get a response. I really can't be sure, but it seems to me that HRMS use a filtering process to pick off the easy help requests first, or maybe the requests that are articulated clearly and concisely with well presented information that makes it easier for them to respond. In that because of the quality of the information presented to them they already have a good idea what is wrong. Just a theory on my part, as I have nothing but my own experiences and reading the reports of others on this forum to base it on.
But all of this is going to nought, if you cannot get your emails delivered to them in the first place. As I said before, gmail seems to get mentioned a fair bit as a common denominator with lost in transit mails.
I do acknowledge, and there have been 100's of similar comments made over the years since I have been on this forum, that RailMaster should just connect over the Internet effortlessly and just work. The issues with RailMaster seem to stem from the fact that it was originally written for Windows XP using the now obsolete Visual Basic 6 and really needs a complete ground up re-write using current Microsoft application writing tools and standards. It is still written in VB6 and has just been tinkered with to make it run on Windows 7 to 10.