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I'm not sure exactly what you mean by no symbol on the dash. Different sensor or TPMS problems will give different indications. Different model years may have slightly different reactions to problems, but in general you'll probably just get a DIC message with a loss of tire pressure.
Several forum vendors can supply you with a new sensor, or you can get used ones on eBay.
Bob's House of Wheels, Parts Taxi, or Gene Culley are forum vendors that can provide you with sensors. Here's an excerpt from Gene's website:
C6 Tire Pressure Sensors
2010 +
15268606 – Tire pressure sensor - $45.45 each
15234846 – Tire pressure sensor nut - $3.89 each
Total set of 4 nuts and 4 sensors $216.70 shipped.
Note: The sensor comes with the washer and valve stem cap.
Setup includes: 4 sensors, 4 washers/o-rings, 4 caps and 4 nuts.
2005 – 2009
25758220 – Tire pressure sensor – $57.78 each
15234846 – Tire pressure sensor nut – $3.89 each
Total set of 4 nuts and 4 sensors $270.85 shipped.
Note: The sensor comes with the washer and valve stem cap.
Setup includes: 4 sensors, 4 washers/o-rings, 4 caps and 4 nuts.
You can see that for your 2005 you'll need part# 25758220, which is a gray colored sensor.
After your new sensor is installed you'll need to have a relearn procedure performed by the tire shop to program the sensors into the TPMS computer memory in the car.