TC35 GSM module does not respond to "AT" command

I had a quick look at the TC35 manual and I think you shouldn't overlook the fact that the serial interface operates at 2.65V. The Uno's serial operates at 5V. Apart from communication problems (also arising from the differences between CMOS and TTL levels), you are running the risk of damaging your GSM module. You may want to search for more information on signal conversion before returning to the software issue.