The Written Torah mentions little about creating a fire on the Sabbath, if I remember correctly. By starting a car, I'd think I would be starting a fire. Is a Jew allowed to do this? Why or why not?
Moses tells the people who are about to get busy building the Tabernacle (sort of a travelling Temple in the desert) that they need to pause all their construction activities on the Sabbath, and mentions for instance not to burn things.
Our Oral Tradition (recorded in the Talmud, tractate Shabbat, see especially Chapter 7) has a list of 39 categories of creative labor which were used in building the Tabernacle, all of which are therefore prohibited on the Sabbath: "growing" (including planting, watering, and fertilizing), "plowing", "reaping", "cooking or baking", "dyeing", and so on and so forth. One of these is, as stated, "burning."
Hence, use of the internal combustion engine is prohibited on Sabbath. That's why Orthodox Jews have to be within walking distance of a synagogue, they can't drive; this creates a geographic sense of community that is very different than what typical American suburbia developed.
People often incorrectly think that the prohibitions in force on Jews on the Sabbath have to do with not 'working'. This is not exactly correct. One may hear people say that "in the old days" it was a lot of work to make a fire (and thus light) but now all we have to do is flip a switch, so now it is not work and is ok to do. This incorrect thinking is applied to many of the other Sabbath prohibitions. The fact is that the the type of 'work' that is prohibited, as someone stated above, is based on the 39 categories of creative activities that were done in the construction of the 'Mishkan', i.e. the Tabernacle (portable 'Temple') that was constucted when the Jews were in the desert after the exodus from Egypt. Those construction activities were halted for the Sabbath. The whole basis of 'resting' on the Sabbath is because G-d 'rested' on the 7th day after the 6 days of creation. Now we know that after those 6 days of creation G-d did NOT say "Wow, I am exhausted! I need to rest!" What that 'rest' means is that He stopped doing creative activity. In like manner he commanded the Jewish people to cease from doing creative activities on the Sabbath. This serves as reminder every week as to WHO it is that created the world we live in and who is truly in control of it. It gives a chance to reflect about the greatness of G-d and all He has given us, and about the limited creative powers that we do have because HE gave us those abilities to use to serve HIM.
not only starting the car, but on it's regular use you are constantly kindling and extinguishing fire, see how a 4 stroke engine works: http://en.wikipedia.org/wiki/Four-stroke_engine http://www.animatedengines.com/otto.shtml http://www.compgoparts.com/TechnicalResources/FourStrokeEngineBasics.asp http://www.howstuffworks.com/engine.htm
a different question is if a non jew could do it for a jew, which is a whole question on itself that depends on when, how, why and have exceptions
No a Jew cannot start a car on the Sabbath for the reason you outlined above. A non Jew could in theory open the car door and drive a Jew around, however there is a concept of marat ayin, where another Jew will see another Jew getting into a car and think, if they're getting into a car, so too can I drive.
Shemot (Exodus) 35:3
לֹא תְבַעֲרוּ אֵשׁ בְּכֹל משְׁבֹתֵיכֶם בְּיוֹם הַשַּׁבָּת
You shall not kindle fire in any of your dwelling places on the Sabbath day.
(Translation via Chabad.org)
This verse clearly instructs us that it is forbidden for a Jew to light a fire on the Sabbath. According to the Rabbinic Tradition, which is binding, starting a car is prohibited as it lights a fire in the engine when it combusts. Electricity also falls in this category.
Devarim (Deuteronomy) 5:14
וְיוֹם הַשְּׁבִיעִי שַׁבָּת לַיהֹוָה אֱלֹהֶיךָ לֹא תַעֲשֶׂה כָל מְלָאכָה אַתָּה | וּבִנְךָ וּבִתֶּךָ וְעַבְדְּךָ וַאֲמָתֶךָ וְשׁוֹרְךָ וַחֲמֹרְךָ וְכָל בְּהֶמְתֶּךָ וְגֵרְךָ אֲשֶׁר בִּשְׁעָרֶיךָ לְמַעַן יָנוּחַ עַבְדְּךָ וַאֲמָתְךָ כָּמוֹךָ
But the seventh day is a Sabbath to the Lord your God; you shall perform no labor, neither you, your son, your daughter, your manservant, your maidservant, your ox, your donkey, any of your livestock, nor the stranger who is within your cities, in order that your manservant and your maidservant may rest like you.
(Translation via Chabad.org)
This verse also seems to tell us that we, nor our animals or servants, should do work on the Sabbath. In my opinion, a car might actually fit into this category, since today we use a car like one would have used a workhorse or ox in previous ages.
Plus we also must remember to keep the "spirit of Sabbath" too. Just because there is a loophole in halachah does not mean it should be done. The purpose of the Sabbath is to rest in G-d's creation, taking pride in what he made, minus our human additions. Sabbath is also for family and friends, spending time together and having fun. And lastly, Sabbath afternoons should be spent over a Chumash or some other religious text, as for some it is the only day one has time to study our Holy Torah! Sabbath is not meant for a Saturday drive.
But it is the engine that kindles and extinguishes the fire, if we were to do it by ourselves we would be better off with horses. In fact starting a car will first run an electric motor which positions the pistons correctly and causes the fuel to be sucked to the combustion chamber and only when the pistons are correctly loaded and positioned the engine sparks the fuel/air mixture. So all of the igniting and extinguishing happens by the engine controller's deference not the driver's. And if it is a diesel engine it won't even produce a spark, the fuel ignites spontaneously when it is pumped at high pressures into the chamber. Botton line starting the engine is the same as giving a command (to a machine, not even a human or animal) to kindle the fire not doing it directly, and as such it is akin to ask a non-Jew to drive you to your destination, only with one less layer in the chain of command. And if the reason is to attend to the Synagogue we can agree it's a very good one.