Invalid sim

Okay, that would mean the iPhone you have is locked to a carrier different than the SIM you are trying to use. If you do not know which carrier that is call AppleCare and tell them you just want to know which cell carrier your iPhone is locked with. Then call that carrier and see what their unlock policy is and if you qualify.

Is that the entire message or is is something much longer?

I don't suppose you could share that message? Does it say something about this not being a hardware problem?

Do they not have AppleCare where you are?

Did you happen to buy this iPhone at Best Buy and used a SIM in it while there? Or where did you buy it? If you purchased it from eBay and they listed it as unlocked you will need to deal with the seller or eBay.