My boarding pass says "TSA Pre" on it, but it does not have a checkmark like in the TSA Precheck logo. What does that mean? Can I still go through the precheck lane?
It means you have TSA Precheck for that flight. Different computer systems will render the indicator differently. I've seen anything from a graphic logo to just the words "TSA PRE" somewhere; many of the systems that print boarding passes are incapable of printing a checkmark.
Compare, for example, this American Airlines boarding pass, with the TSA Pre✓ logo, with this JetBlue one with just the words "TSA PRECHK" and this Southwest one with just "TSA PRE." It's not even consistent within one airline: it may look different depending on who printed your boarding pass or whether you printed it at home or used an airline's smartphone app. The important part is that if the boarding pass says anything about TSA Precheck on it, you have it for that flight, whether there is a literal checkmark or not. The information can be encoded into the boarding pass's barcode as well, so it can be verified no matter what information is printed on it.
Show the boarding pass to the person controlling access to the Precheck lane at the checkpoint, and they will direct you accordingly.