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Modem can draw up to 2A. So if you supply pic and modem from same power supply maybe voltage drops and lock your pic.

If you get once reply from modem, your hardware was ok.
Is anything was wrong you won't get reply if you restart or not...

I'm have board with sim900 connected to pic. Modem have 4V supply, pic have 3.3V.
SIM900 use TTL 2.8V true uart, not inverted. I put just 2 resistor in series with comm lines.
If you connect modem...

Usb-TTL serial module use true 3.3V uart.
You port setup was ok, because you menage to get signal from modem, to pic, and send it to pc from pic...
Also TX from pic is ok, because you get...

Maybe problem is in supply voltage. Modem works on 2.8V(it have internal regulator), so pic should work on 3.3V, and you must have serial resistor on pic TX. So modem can't draw any current from pic...

Try to connect PC to PIC, instead of modem...
Also use Rx on PC board to sniff what is happening when pic and modem communicate...

Check does it send correctly with HT. Use your usb ttl uart converter board.
Try to send CRLF then pause 100, and then send command...

Try
HSERIN [WAIT("CSQ: "),DEC Signal]
SEROUT2 ....[DEC Signal]
You don't have 13 chars, after AT+CSQ:...
From manual
STR ArrayVar\n{\c} Receive string of n characters optionally ended in...