I'm another in the camp that anything's OK in moderation, if it doesn't interfere with other important life skills. When I was home with DS6, he was a very high-needs infant and toddler, who also did not like to nap. I'm all for finding things that can provide a break for mom. I can't remember exactly what age he used the computer (I'm sure I could search this site and find something!), but I would somewhere between 1 and 2, he wanted to use the keyboard. I opened a blank screen on Word, and let him go. We called it the smiley-face game (I showed him how a colon and paren made a smiley-face.) Sometimes I'd switch the font to wingdings, and he loved that. I've always had a rollerball (stationary) mouse, which DS could easily use at a young age by using one hand to roll and the other to click.
At 18 months, DS's grandma got him a leapfrog count and learn math desk, which he loved. He learned his numbers 1-20, and some basic counting stuff, and played with that quite a bit.
I think between 2-3, DS was pretty independent with the computer. We saved pbs and nick jr and other kid sites to his favorites. We got him some education pre-K/K software, and he loved that for awhile.
Your comment about the repeating of pages of books makes me thing that your little one is starting to crack the reading code. I remember the reading-the-same-book-over-and-over-stage.
