Can't activate iPhone 4S
As a rule of thumb, you should always prevent buying iDevices(iPod, iPhone, and iPad) from Craigslist and eBay, no matter how attractive they look. Even if you had went through eBay, you couldn't raise a dispute since the device isn't physically defective.

Your best bet now is contacting Apple, and I do not think they would give you the Apple ID. Have you tried contacting the person you purchased it from?