Again, just guessing..

Maybe the module is sending something but not what is expected.
Try moving the LED feed back to the beginning of the routine to see if it is stuck there.
Code:
GSM_SIGCHECK:
High PORTB.0     ' 1st LED on
PAUSE 1000
low PORTB.0
PAUSE 1000


HSEROUT ["AT+CSQ",13]                    'Send AT to modem followed by a CR
HSERIN 4000, GSM_CHECK, [WAIT("AT+CSQ"),STR Serialdata\13] 'Check OK reply, wait 5sec max.
Serout2 PORTD.5, 84, [$D, STR Serialdata\13]
RETURN