Miriam,
Thank you for looking into our problem and spending your time to do some research. I am currently in Washington DC but my LA fleet manager will be back for work on Monday I will ask him to do the search and get back to you right away. I did the same thing you did from Washington DC and when searching for "car service to lax" I get exactly the same result as you. There are there pages for the local pack but we are no where to be found. In organic I see our url ranking in #4 on page 1 that might be a bit biased as google might rank us higher since it knows we always click on our url. I also conducted another search just for fun.
I searched for "car service from lax" the same thing almost except instead of "to" we use the word "from". I see our site on position #4 but in this instance there is no local results. Google shows local results when searching to LAX but not FROM.
The only way I can see our business in local results is by searching "car service los angeles" I find us on the page 4 of local results.(4th tier). Again a terrible place but at least it comes up. To tell you the truth I am not much worried about the local at this time, I was just confused why the organic result is such a mess. I think if we get an office close to LAX we will fix the problem with local results at least I have that feeling but I just can't understand the organic situation at all.
I will write to you again Monday or Tuesday with our findings. Again thanks a million and enjoy your weekend. I think if we get an office close to LAX we will fix the problem with