You will almost certainly need a permit to run new wire unless your municipality is really weird, and they're typically weird in the opposite, more authoritarian direction. It's not hard, expensive, or particularly onerous, but you will want to make sure you get the permit if you do decide to DIY. It's cheap insurance to prevent a house fire not covered by insurance due to un-permitted electrical work.
Sokoloff's alternative is the easiest and by far the cheapest. If you have metal conduit and metal boxes, with the conduit going from box to panel with no interruptions, then you can use the conduit as your ground carrier according to the NEC, but your municipality very well may have different rules for this. You would need to call to confirm if this would pass. However, you could probably do this without a permit anyway, since you'd just be "fixing" the existing system instead of new work.
Otherwise, you're pulling all new wire. Have you priced copper yet? Because you need to be prepared for how much that copper wire is going to cost.