The best replacement for a broken set of un-amplified rabbit ears is... another set of rabbit ears! Get something with a loop between the two ears, like this:
The loop is for stations broadcasting on UHF.
Having an HDTV makes no difference if your old rabbit ears got you good reception before they broke. These antennas are capable of picking up analog and digital TV signals equally well. The "made for DTV/HDTV" label is marketing hype, nothing more.
I recommend the Radio Shack 1874 Budget....in an unamplified Rabbit Ear & Loop. This one has the best designed loop for UHF television frequencies....its just a bit larger in diameter than most others.