Q: 3G got wet and screen doesn't respond

I dropped my iPhone 3G in water, but it was only submerged for about 45 seconds. I got it out, turned it off and took out the sim card. I quickly dried it with a towel in put it in uncooked rice for over 24 hrs. It turns on now and the screen is normal, but I cannot do anything with the touchscreen. It's like it's not working anymore, but I see no damage. Do I need to pop it open and clean the logic board and stuff, or do I need to replace the entire screen? It's a used phone, so I have no warranty anyways. Any help would be appreciated!