Transmission will not shift past second

My wife hit a deer and the impact damaged the transmission cooler radiator and caused all of the transmission fluid to leak out. She continued driving the car for another about three miles at which point the transmission quit working. I had it towed home and fixed it up including putting in a new transmission radiator. I replaced the transmission filter and fluid. In the process of dropping the pan, I managed to break the shifter cable that runs alongside. I have since replaced it, however the car would not go into any gear (it just kept revving). I realized this was due to low amount of transmission fluid even though I filled it up to the marks on the stick, it must have gotten sucked and circulated into the radiator or elsewhere and the level went down. After I added more fluid I finally got reverse, first, second and drive. The problem is, in drive, it will not shift past second and the car will not go more than about twenty five mph. If I try to go faster, the engine will just rev up and then it will take some time for second to engage again. Any ideas of what this could be? It is a XL Denali with a 4L60E transmission. Could this just be a faulty solenoid?