well there are many ways to skin a cat, so i would start with the simplest where patience is the key.
go to hobby store pick up a sheet of abs, and lexan sheet, take a hot knife, or a butter knife hold it on fire till it gets hot, and melt cout out the shaped, the 3 M bars, and the opening for mp3player screen, you pretty much only get i chance to do it straight, and right.
don't throw away those pieces you cut out you will need them
sand it, so it looks okay, with no smudges from both sides
take out lexan sheet (acrylic glass only easier to work with), cut out bars to put in bar cut outs. you can use superglue, or transparent epoxy to attach them
take another lexan transparent acrylic sheet, sand it with 200+ grit, take a drill about the size of the LED, and drill a 2 holes to insert LEDs into., you can attach leds with hot glue gun, epoxy whatever transarent, no superglue single it's a solvent and it might damage LEDS
time for a test, wire leds with 390 ohm 1/4watt resistors, and test them with the regualr 9 volt batteries
if you need more info on LEDs this is a great site
i am not gonna explain electrical as much, i am not here to spoonfeed you all the way
get some brass strips, and attach them to the ABS door, those will hold you mp3 player @ place
get some small hinges, and attach them with epoxy to the little door, and with screws to the base, the the hinges with remoable stemthat way you can separate 2 pieces when you need to work.
the last stage
take the unused abs trips you were about to throw away, and go to home depot to buy fiberglass resin hardener they are about $4.00 for a tube, buy 2 just in case.
cut them is small pieces into the the cup, add some fiberglass hardener until it becomes a sludge, apply it on the back of the door to even things out, and get rid of inperfections, and cover up some things, snad it till smooth, paint if necessary, attach the player, and the wiring for leds.
I would wire leds to ingnition fuse sinche they don't need much amperage, and will glow as soon as you start the car