Solve Chess. I'd ask the computer to analyse every possible position and determine if White always wins or Black al;ways draws or if the game is only determined by certain openings. I'd also ask to see how many digits of Pi it could muster up. With infinite speed and internet I'd have it search the entire www and formulate its own version of AI. 24 hours at gigabit speed could analyze the entire www. I'd have all the unsolved math problems that I could research with me (some of them have Million dollar prizes) I'd take along the uncracked codes of fame as well. At this point we have only looked at the chapter headings of DNA. I would like to unravel the "Book" that appears inside the cells and gain the trapped knowledge residing in each of us. But this is ridiculous, what infinitely fast computer uses OS of today? I think the limits in DETAILS are just meaningless, I would have the computer WRITE new software that would run at its own rate. With infinite speed it could run through all possibilities and write its own software with the twist of a wrist. I'd map out evry possible universe and every possible situation and run the results to determine what will be the outcome in OUR universe as well as all the other ones possible. That would leave me with a whole bunch of time, so then I would get wild with it and remain as creative as I could trying to gain as much for humankind as I could. I'd upload to cloud, who needs hard drives. I'd interconnect with other computers, 16GB ram haha. I would do the whole world the ultimate favor and by the next day the world would have changed forever.