Update on this post about my Garmin Forerunner:
I just tried it again, and the god damned thing did the same things as before – it took almost exactly 5 minutes into a workout to start showing my heart rate. After the workout, I waited until I had recovered and turned off the GPS and turned it back on, and again, it says “HR Monitor Detected” but no heart rate showing even after twenty minutes. I tried changing the battery in the heart rate monitor strap, no change. Dammit. Time to try some electrolyte gel, I guess.