where was this company started?
1856
Rogers Locomotive and Machine Works
Rogers remained president until his death in 1856 when his son, Jacob S. Rogers, took the position and reorganized the company as Rogers Locomotive and Machine Works. 
who started rogers locomotive and machine works? Thomas Rogers, Morris Ketchum and Jasper Grosvenor. when? 1832
wiki:20644265
Rogers Locomotive and Machine Works [SEP] Introduction
Rogers remained president until his death in 1856 when his son, Jacob S. Rogers, took the position and reorganized the company as Rogers Locomotive and Machine Works. The younger Rogers led the company until he retired in 1893. Robert S. Hughes then became president and reorganized the company as Rogers Locomotive Company, which he led until his death in 1900. Rogers avoided the American Locomotive Company (ALCO) merger in 1901 through closing and reopening as Rogers Locomotive Works. The company remained independent until 1905, when ALCO purchased it; ALCO continued building new steam locomotives at the Rogers plant until 1913.