What you want to get is a reel of
led strips.
I just started playing with these recently, and they are amazing. You can grab a 16 foot reel for around $14 giving you plenty to use wherever you need. It is directional and probably the slimmest light source you could ever use for a marquee, probably less than 1/4" thick.
I used it to ad light to my kitchen by running it along some molding, going to add it to the underside of my stair handrails, and soon will be attempting something really crazy involving my cab although saving the reveal for another time.
As for power, look in your box of old electronics. You probably have a 12V power source you can use to power it laying around.