Your battery may be getting weak. The starting current is dropping the voltage causing your speedo not to work. That is why it works if you run down the road, stop and restart. You can also keep your battery on a tender. This happened to me even though the bike started fine. The BDM battery was original and 3 years old. I use it on my generator now. There was a flash to the EHC to reset the speedo after starting. I kind of liked the fact that it was a tell tail sign of a degrading battery. Once, I replaced the battery with a Braille, I had no more speedo issues.
Having said this, putting in a Dakota Digital is a piece of cake and has great features and accurate speed in every gear which I only had in 6th gear on the BD speedo. My original speedo now lives in a spare parts box.