The first thing to do in troubleshooting is to make sure its on. On can also mean put in correctly. Make sure its going in like this:
Once we know its on, we need to make sure its clean. Just using a can of air, or maybe even blowing into the SIM card reader, try to clear anything in there. Just blow into it gently, or use a can of air. If its clean, make sure the SIM card is clean. Don't ever use water or any liquid to clean it.
Since it seems to be an issue with the SIM card or card reader, I would ask your carrier for a new card. There may or may not be a charge affiliated with this, but I can not say for sure. If afterwards, your iPhone still can not see the SIM card, then it may be the SIM card reader inside of the iPhone. Again, your carrier may replace the phone for free. If not, then you can sell the phone on eBay. People love those phones. They are fast iPods (or relatively fast for an iPod) and have a working microphone and a decent speaker. Then of course you'd have to get a new iPhone, which would have the strings attached of renewing your contract and paying out of pocket.