To diagnose a problem with the port, try using a different battery and cord for a while. Damaged Power Cord. The power cord is a wire inside a plastic sheath, and the wire can break with or without damage to the sheath. If the power goes on and off as the cord is moved or bent, the wire is likely broken.
You can work out if you're sore. Don't exercise the same muscle groups that are hurting. Do legs one day and exercise your upper body the next. By doing so, you'll still be able to get exercise and allow your lower body to recover and rebuild.
Work out: This may be just a sign that you over did it. Fatigue after a workout is not uncommon. Take some anti-inflammatories, stretch well, and ice your legs. It may be that you hurt more tomorrow than you do today. As long as it is not getting worse, just watch it and decrease your workout intensity until you are back to baseline. Otherwise, see a doctor.