Do the chassidic jews accept help from shabbos goys on Saturday?
Yes, all the time.
Although they usually do violate the Shabbat when doing so. It's very tricky. You aren't allowed to as a gentile to be
Mechallel Shabbat for you, but you can hint it. The problem is how to do it. Personally, my family never has asked a gentile to do anything for them on the Shabbat.
In Boro Park, on the holidays and often on Shabbat, NYPD Cops while patrolling stop into Synagogues and ask them if they need an AC turned on or if anything needs taking care of. This is usually arranged by the community affairs cops.
Another issue with asking a "Shabbos Goy" to work for you on Shabbat is because how do you know if he is a gentile. He may be a secular Jew or a Jew that converted to X-tianity.