If I left food out of the refrigerator for some period of time, is it still safe? If I left it out too long, can I salvage it by cooking it more?
When in Doubt, Throw it Out!
You cannot see or smell bacterial contamination. Mold that appears to be growing only on the surface may grow invisible roots into softer foods. Do not rely on a visual inspection or "smell test" to tell you whether or not a food is safe. It's not worth the risk - food poisoning can be much, much worse than an upset stomach.
The Danger Zone
Why does cooking not completely "reset the clock"?
Regulation and Risks
Follow the guidelines set out by reputable regulatory agencies, especially when serving others. Local organizations include:
Other regulatory sources apply in other parts of the word, but major food safety organizations usually agree in essence (if not in complete detail) on most issues.
Failure to follow reputable guidelines is irresponsible if you are serving guests, and failure to follow your specific local codes is likely to be illegal if you are serving customers.
Health codes tend to be very conservative, to fully protect the community. You have the right to take risks on yourself by ignoring their recommendations, but please do not risk the safety of others.
Again, When in Doubt...
Once again, if you suspect spoilage or contamination, please, throw it out.
* Note: this is the FDA's rule. Other agencies may have variations on it. Additionally, government agencies generally make very conservative recommendations - they're trying to make sure that no one who follows the rules gets sick. Breaking the rules means maybe taking on some risk. That's up to you - just remember, eventually someone gets unlucky, and food poisoning is not fun.
Further Reading/Frequently Asked
The question was: "If I left food out of the refrigerator for some period of time, is it still safe? If I left it out too long, can I salvage it by cooking it more?"
Answer: It depends ...
These are just a couple of questions so you get the general idea that it really is impossible to give a generalized answer to the question.
Considering that only a surprisingly small percentage of the worlds population actually has access to refrigerators and people still eat I think it might be obvious that refrigeration is really not the only way to store food for later consumption.
For a more in depth study of the topic I recommend:
As a more general tip I would stick to common sense. e.g. any food containing raw eggs (Mayonnaise) or food that must by its nature be considered contaminated (store bought raw chicken / raw meat) needs to be handled in a reasonable matter (you should be able to find the correct advise about handling these kinds of foods in any good cookbook) to avoid colonisation to an unhealthy (when eaten - even after cooking) point. On the other end of the spectrum leafy vegetables or fruit bought fresh from a farmers market actually comes with its own protection in the form of beneficial bacteria on the skin and is therefore less likely to be easily (meaning in a short time) colonized by pathogenetic organisms. Learn about your food and learn how to cook and you probably will be safe.