My 2000 Honda CRV was parked in the garage for 4 days (outside Temperature average 1 degrees celsius). On the 4th morning I tried to start the vechicle. The lights barely came on and the starter did not turn. I replaced the battery with a new one myself. Tried to start the vehicle. The lights burn brighter and the starter turns but the engine does not crank. Any suggestions on what could be wrong? What can I do?

If you are saying the starter motor cranks, but the engine does not start, I would focus on the distributor. Normally, replacing the Ignition Control Module (ICM) and coil solves the problem. Be sure to apply a thin, even coat of silicone heat transfer compound to the back of the new ICM.