Only time will tell. You could bring in a consultant for a more informed opinion, but it will be still be just an opinion. If there is no other source of ground water and the run-off was adequately managed, it will eventually dry out. It's possible to drill a small, shallow monitor well to determine if there's a shallow water table problem. If there's any water at all, by monitoring over a period of time, it can be determined if it's accumulation slowly draining off or something more permanent that needs to be addressed.
I had to draw a small diagram to see how the area was around the house. I drew a swale in to show what is there already, or hopefully something that can be created
![enter image description here](https://i.stack.imgur.com/2XwEi.png)
What looks troubling here is the concentration of runoff heading to the house IF there is no swale there, that is why I hope there is one there, if not you really need to get the flow away form the house. It is bad enough that it is sandy, the water can still perk into the foundation, though it will be minimized with a swale. The clay base on the north side, sounds exactly as you describe, a bowl.
You need to do whatever you can to minimize the water infiltration, to start. It may not require to pipe the downspouts away from the house to a drywell or into a French drain, well not a French drain as you may plan around the house. French drains return the water to the ground, and in turn the crawlspace. What I mean is terminating the downspouts into an in ground pipe that daylights downhill of the home. A drywell would work too, but it is much more than may be needed.
This is the minimum I would suggest, although it is still a lot to do. I would also consider waterproofing the foundation, it may work on most of the foundation, but I think the runoff would still migrate under the foundation on the south side since it is still on sand/ clay mix presumably.
All of this is still tempered by the symptoms created by the water in the crawlspace. If there is no evidence of black marks (mildew) or white fuzzy stuff growing in places from the excess moisture in the crawlspace, if none of these symptoms exist, al least extreme measures are not needed. Regrade if needed, would be the minimum, downspouts to daylight away from the house the next active remedy, drywell addition the next, and if you are doing all that digging, waterproof the foundation, all these measures combined are the extreme I mean.
![enter image description here](https://i.stack.imgur.com/ELVDq.png)
Edit 1/26/13
Aside from the shape of the house and other extensions from it, it shows the same thing happening except your swale that exists is more of a collection point. It appears the rain runoff takes the same path, but the house is in the way. The swale in the above sketch I posted would divert the rain water before it gets too close to your home. Is this a possibility to happen? It can be done by lowering the grade or if the house is high enough above grade, the grade can be raised, but that has implications too. The water in the swale may be of no concern. I would draw more concern to the south and west side where the rain looks like it is path is unencumbered to the foundation.
I will edit your drawing to show a more accurate idea and post it.
Back at the downspouts that I mentioned earlier, if the grade looks like it can daylight a underground lead would help reduce the amount of water at the foundation. Yet the addition of the swale will redirect the downspout water as well.
Best Answer
Asphalt driveways are surprisingly flexible when new, and residential driveways are not typically compacted much past 90% — which means there is some flexibility to rework and further compact it.
I corrected a high edge on mine by heating with a torch and pounding it with a 4x4 hand tamper I kept coated in non-stick cooking spray (to prevent soft asphalt and aggregate from sticking to the tamper).