Any good computer toys for ages 1-2?

My daughter is absolutely fascinated with our computer and iphones. For Christmas I would like to get her a toy computer and am wondering what you have found the best for really young children (ages 1-2 years)? I would prefer it to actually have a screen and not just be shaped like a computer.

I know leapfrog sells some products like this but I would like to know exactly which products you have been really impressed with or that your young kids have loved - any brand!

When I was six I got my first computer my siblings and I shared. It was this giant old thing lol! There was no Internet, and no way we could connect it to the Internet so we couldn't see inappropriate things. We had our own computer games we got every year for Christmas and birthdays, they really piled up since I have two other siblings plus me and we all shared them! It was save because it was a giant box-like computer, wasn't flat screen, so I couldn't move it easy. No Internet so I couldn't see bad things or images. We all shared one account, and we had to ask permission first and my parents would type in the password for us.