SAZABI

First, if I were you, I wouldn't even leave my car to some shop that i don't know without sorting everything out 1st.

ok... back to your case.  For mechanics, they have books indicatiing how many hours it would take to do certain things on specific car.  So, they don't need to take out everything before they can give u an estimate, if you can describe precisely what needs to be done or what the problem is.  And I can tell you that the time indicated is usually more than enough for the job.

If you don't know what needs to be done, and the mechanic needs to find out before he/she can give u a quote.  They can always give you a call after they find out.  If you decided not to fix it at that time, you will likely need to pay a inspection fee (which is roughly $70 - $90 per hour).  

Well, i guess there is nth u can do now.  Next time, just take your car away if they refuse to give you a rough estimate lor.