I totally agree with tanza, you have to let them cry it out. Start working on habituating the puppy to you leaving. For example, put her in the crate or whatever situation you are using and walk out the door. Stand outside for five minutes, then come back in a reward her. Work on gradually increasing the time you are gone. As you work on it, make sure that you start to differentiate between rewarding behaviors you do and don't want. You don't want to come in and give her a bunch of treats for howling like a banshee the whole time you were gone, but in the beginning she may need that just to see that you going means you coming home and treats 
You want to associate your return with good thoughts.
You also have to remember that she may see lots of things a rewarding, which will in turn, reinforce her behavior. If she is crying in her crate and you even talk to her, or let her see you, that is rewarding. If she cries and you try to comfort her you are rewarding her crying, she got what she wanted. As you learn how to work with her you will start to learn how to outsmart her, it just takes time and lots of trying different things. See what is most rewarding for her, sometimes it may not actually be a treat, it may be a toy.
Since you live in a condo, you may want to talk to your neighbors if she is making lots of loud noise for a long time. I have heard stories of people calling 911 because they think someone is screaming. Talk to them and let them know ahead of time and they may be more likely to take an issue up with you rather than someone who may take action.
You aren't bad parents, we all went through it. The work required to raise a basenji is significant but it is rewarding. I often liken it to a toddler and people laugh, but when they are involved with us and see how much work it is, they begin to understand.
Good luck!
