It sounds like what you're saying is that you have no Internet access, not that your SIM card is malfunctioning. What you need to do is make sure the phone's internal settings allow for access to Cingular's Media Net. So, first off, do you have a data plan? That being said, you may be able to get the settings from Cingular customer service.
I have an unlocked cingular branded LG F9100 cell phone, using an AT&T sim card that I had from a previous phone. The voice part works fine but the data isn't working properly. Could my phone be reprogrammed so I could effectively use the AT&T sim card?