For example if you have a website called "getfreecars.com" and someone types in google "get free cars", is google likely to show this site as first? i know that there are many factors such as backlinks etc but to answer my question, is it a yes or a no?
Yes if you are having equal strength in backlinks other factors. Only domain name will not help. For example, if you have two websites which have got all other factors equal, then one with domain name will get higher ranking. It is safe to assume it this way. Some may say, you will stand ahead even if you are falling short in other factors, but by what margin can not be said.
It can play a big role like rash said, but you still need to build backlinks and content on your page to rank. Simply having the domain name will earn you kudos, but you need more then that.
Yep I agree with youhoo, it has a massive effect and getting a good domain name is half the battle. To purcahse a Domain Name I recommend GoDaddys.