Can I get an entry level cook job without going to culinary school?

Absolutely!
In fact it is the best way to enter the field.
Good Luck!

Depends on whether you can find a restaurant owner that is willing to take a chance on you.

Yes you certainly can .

Absolutely. I would venture to say that MOST entry level cook's positions are filled by people who have never been to culinary school. I certainly didn't, nor had most of the cooks I have worked with over the years.

If you were in a culinary school they would reward you with the same job for credit as internship. (probably make more money doing it too)

Im a qualified chef, and i took the better paid route, albeit a bit longer than doing school or an apprenticeship. I started off as a kitchen hand/cold larder, doing food prep and cleaning, and just kept moving up in that one resteraunt, as the positions became available. Until i had been working as second chef for a year, then the chef i was working under, helped me get the qualification paper work organised. That was until i got pregnant, and couldnt stand working in a hot, busy kitchen, so i moved to front of house, now im the bar manager in a busy hotel/resteraunt.

your best bet in a situation like this is to go to a chain that doesn't require you to have any experience..something like chili's or a cracker barrel . once you get in there go up the chain a little bit and learn as much about the back of the house and you can. a more reputable establishment will be more likely to take a chance on you if you have some real experience even if you don't have the school behind you.