Yes, monkeys could type out the zeros and ones. In fact we (not the monkeys) kind of did. There is a library of babel for audio named the sound library of babel which contains every 15 seconds audio recording you can imagine. Every single one. Almost all of them are white noise, but still there are recordings of every human saying any words in 15 seconds.
Some addition to my post: The computer I found is a Fujitsu Esprimo Q957. I’ve read online that they are very power efficient and don’t draw as much. I will probably run some lightweight task almost 24/7 and sometimes heavier tasks for short periods of time. A raspberry pi is for me too expensive for the average specs, even if it is very efficient. I think a upgradable pc or mini pc is best, because they are cheap, but can be easily upgraded without buying a whole new computer.