"No reply on AT command ATE1" error message when opening TGSM session.

Bad baud rate is probably used. Module does not use autodetection or rate differs from default one. S25 have probably 19200 set in TGSM as default rate. You can override it. The best place is set TGSM.ComDevice.BaudRate in TGSM.ComDevice.OnBeforeOpen event.

Module baud rate may be changed using AT command (AT+IPR), as well. For example AT+IPR=0 is autodection. See module AT commands specification.

You can test your baud rate manually. There is combo box to setup baud rate in GSMCENTER. Set a baud rate, go to modem log and write 'AT' via keyboard, if modem will respond your baud rate is OK, if not check another baudrate (you can check it of course in any communication program).