Actually, you can swap SIMs on an iPhone without powering it off - but Boo's advice is good. Power-cycle it. But you won't be able to swap SIMs unless the phone has been unlocked... you don't mention if it's unlocked or not, but locked phones require a specific SIM from AT&T (that comes with the iPhone). You can't just put any AT&T SIM in - unless it's been unlocked.
Check the headphone jack - despite the recessed nature, there's been some failiures.
Check the IMEI of the phone matches the number on the back of the phone - there was an unlock bug that screwed up the IMEI.
I'd also check the firmware version and how they unlocked it. The first round of 1.0.2 firmware unlocks messed with stuff best left alone, the second round of unlocks is more reversible. So if the phone was unlocked with the original unlock, it can be a complicated flow to undo this.
So if the phone is running firmware 1.1.1 then it was unlocked with the newer method(easiest check is just to see if the purple iTunes icon is on the screen, but you can also dial *5001#12345#* (field test code), or go to Settings -> General -> About.
If it's running 1.0.2 and was unlocked with the "original" method (and not Anysim 1.1 or IPSF) then understand that it will likely be a bit of work to get it to 1.1.1. "Virginizing" as they call it, is not a simple process. There's no harm in running a 1.0.2 with the original unlock, but it's a bit of a pain to upgrade.