main power voltage drops

I have an old 1987 Honda Accord.  When I try to start the car and turn the key into ignition position, the lights on the dashboard show very dim, the clock and cd player don¡¦t even work. When I turn to the cranking mode, nothing happen.  I tested the starter wire, no voltage on it when I turn the key to the cranking mode.  Also, I tested the main power cable, the voltage is below 12V.  But the funny part is, after a long period of time, it voltage suddenly comes back to normal 12V, but the car still doesn¡¦t start and the voltage drops again.  I tested the battery, which is fine.  Does anyone know what can cause this kind of rare problem?

I am not sure if it¡¦s okay to post this kind of question on the forum, but I really appreciate for any help.  Thanks!

sorry about the post above, dont know why it shows html code, but here is what i want to post...

I have an old 1987 Honda Accord. When I try to start the car and turn the key into ignition position, the lights on the dashboard show very dim, the clock and cd player don't even work. When I turn to the cranking mode, nothing happen.  I tested the starter wire, no voltage on it when I turn the key to the cranking mode.  Also, I tested the main power cable, the voltage is below 12V.  But the funny part is, after a long period of time, it voltage suddenly comes back to normal 12V, but the car still doesn¡¦t start and the voltage drops again.  I tested the battery, which is fine. Does anyone know what can cause this kind of rare problem?

I am not sure if it¡¦s okay to post this kind of question on the forum, but I really appreciate for any help.Thanks!