Ok, sorry for taking so long to respond. What you will need to project the image is a Biconvex lens. Basically a magnifying lens minus the handle. Usually they aren't too hard to find, depending on the size you need. You will use that lens to build what's called an opaque projector. This is a projector that blocks outside light so the image you are projecting is cleanly back lit by your light source.
Basically want you want to do is put a light behind a transparency of the image you want projected and a lens in front of the image. You will need the focal length to determine how far away the lens should be from the image and how far away the front of the lens should be from the ground. It is that simple of a concept, the complicated parts are getting the parts. Once you have the, assembly shouldn't be difficult, installation on the other hand could get tricky. That's where the audio install shop would come in handy, they will have the experience to fit the whole thing in the door and wire it up.
You will need:
-An LED for a back light (This includes heatsinking and a driver. You will probably want an XML for it's efficiency.)
-A very small transparency of the image you want to project (Look around town, you should be able to find someone who can make one for you. Check places like local print shops.)
-A small biconvex lens (I would look online for the size you need)
-And a small container to house the whole thing. ( A PVC pipe should do the trick.)
The hardest part of this will figuring out what size transparency and what size lens to get. If I understand it correctly the equation in this case would be:
Distance you want the image to be projected X Size of your transparency
____________________________________________________________= Focal Length
How big you want the image to be
This is a detailed explanation of how it's done properly
http://www.projector.com/resources/projectionlenses.php. I don't know the turn around time but you can email them under the contact section to get more detailed help. Or maybe someone here knows a lot more about lenses than I do. You could head over to physicsforums.com and ask for some help, just tell them what you are trying to do and ask for help on the lens size and focal length. I know from playing around with some magnifying glasses that you will want a smaller lens because it makes the image larger and in a shorter distance. They should also be able to tell you a good size transparency to get. Calculating the focal length and lens size is something I don't really know about and I don't have the time to learn right now because I am heading out of town and will not have access to the internet. If you don't figure it out by the time I get back next week I will sit down, learn all this, and help you out with calculating the focal length.
The rest of it is the easy part and puts me back into familiar territory. After you figure out how far the image has to be from the lens you need to build the housing. The easiest thing to do would be to cut a peace of PVC pipe to the right length and plug the various parts in. I think it will work for projecting the image with out distorting it to badly. If it does not work, then the next easiest thing to do would be to build a small box out of ABS plastic sheets. Shouldn't be that difficult for you to do and you can find tutorials on youtube for visual help. I assuming that you have the knowledge and skill to build the box so I won't explain it to save time, I am in a bit of a hurry.
The back light is usually an incandescent projector bulb, but those draw a lot of power and run hot. So you will want to use an LED to save power, heat, and size. A neutral tinted XML plus a single mode driver mounted on a round aluminum heat sink will work beautifully. You will need to know how to solder the wires to the LED's base and to the driver. That's the only skill involved there. The people here will be able to give you the links to suppliers for everyone of these items. You have definitely come to the right place for figuring out the lighting end of things. The only constraint that I see here is the diameter of the PVC pipe will limit the size of the heat sink. Also, a single LED may not provide enough light to compete with daylight. You may need to have a few of them mounted to get enough light to make the image visible during the day. It will make the lighting a little more complicated, but we can help you with that easily enough. Oh, I forgot to mention that you want the light to be very floody. I would put a piece of frosted glass (or plexiglass so it doesn't shatter) in front of the LED's so the light is smooth and even. Also, that should prevent the lens from projecting the image of the LED itself instead projecting the image in front of the LED.
With the transparency you just want to look around for someone who can print them and bring them a copy of the image you want turned into a transparency. You may need the copy to be digital or physical so be prepared for both possibilities.
The lens you will probably have to buy from online. But before you can buy one you need to know the specifics first.
Focus on the lens specifics before you go any further. With out knowing the various distances to mount things and sizes to make them you can't really make anything. After figuring out the lens I/We can give you the specifics on everything else. I can walk you through the steps of the installation but you will need to figure out what wires to splice and where to run wires because you have the car in front of you and I don't. After it's installed and working, I have it in my mind to have the projector turn on when the door opens. There are a few simple ways to do that and we can discuss them when we get there. (If you would rather use a switch, or have the ability to use a switch, let me know. It won't be that difficult to add.)
This is a general plan of what you want to do and not a specific plan because there will be snags along ever step of the way that will need to be figured out before the next step. I cannot predict the specifics of those snags so I am not going to try. Step one is finding out what size/ focal point lens you need. After that we can get to the lighting and mounting, then the install. I will be out of town as I have mentioned so I won't be responding for a short while. Sorry to leave you hanging like this, but the good/bad news is that this is going to take sometime to figure out before you get building. If you are still interested in my/our help still, you'll get it. Hopefully this helps you get a little better of an idea of what you need and what you will be doing.
P.S. Please excuse spelling and general grammar as this was typed in a hurry and not really proof read.