Java / AI / ANN

so, here is my problem:

i'm currently developing a two player logic game in university, and i'm facing a huge problem. The game is a state space representated, and I alredy have Alpha-Beta pruning and MinMax algorithm implemented and they are working fine.
The root of the problem is that my gametree is extra large. It is a 20*20 square grid field, which is actualy a 20*20 JRadioButtons. In every turn, a player can almost select any buttons (not the ones that are already selected and a few other ones), so my searching algoritms create a huge gametree, with only a depth of 4-5 (which is really low) there could be billions of treenodes, and it takes forever to go through all of them, even the A-B pruning fails.
So someone gave me the idea that I should use neural networks, so that way I would be able to do something in real time, but i have no idea how should I even start it and what should I do. I've read a lot about ANN, but still, I have no clue how to begin this. I've  only found a game which implements an ANN for the AI, but it's in C++ and I could't understand it perfectly.

So, any ideas what should I do, where should I begin or WTF to do?

thx

if you want a pic of the game I can show you 1 if you guys didn't understood a word what I just wrote :D

You have exams this late in Hungary? When do you get summer vacation?

Also if you've had stable sufficient sleep rest of the week I've found it doesn't really matter how much sleep you get the day before the exam as long as you get some sleep.