I live in an Area where Most People are nonjews. I can use a Train without Money. And some Rabbis allow to Drive to shul, some not. I live in the Moment to far away from the Shul to participate. Should I pray at Home?

ב"ה Shalom You did not leave many details in regard to your location and community and I wish I can assist your more. Without those details, I refer you to what was written on this site, by Rabbi Sperling who spoke about this issue at length and I concur with what he wrote. See: http://www.yeshiva.co/ask/?id=5356. I just wish to add that in the book Tzeda Laderech pg. 113, Rav Yeshayahu Shapira writes explicitly that one may not travel by train even if driven by a non-Jew , even at the price of praying at home and not at Shul. Furthermore, he added that this has been the custom of all Jewish communities. However, he does point out that in extreme cases as long as the ticket is not being carried or paid for on Shabbat, it has been allowed . It should be clear though, that using a train in such a fashion is only if the train does not leave the confines of the city, because if it does then it is not allowed due to the issue of "Techumin" which forbids us on Shabbat to go out of the confines of the city more than 960 meters even when simply walking.. (2000 Amot) Driving a car on Shabbat is absolutely forbidden and surely out of the question, if not in the case of an emergency G-D forbid. In the book Mareh Habazak (Volume 5:34), it is written though, that if there is no choice and people would in any case travel by car, than the Rabbi may suggest to an individual to use the train in the above fashion as an alternative to desecrating the Shabbat by driving to shul by car. So in short, it is best to personally consult a competent Rabbi to view your specific situation to give you the best Halachic guidance. All the Best