I'm curious if I can find a way to connect and control this thing:
This may be a repost, but I don't know the name of the connection to search for it.
Is it some kind of tape connector?
I think the connector is a Hirose BM10-series FPC (flexible printed circuit) to Board connector:
http://il.mouser.com/knowledge/interconnects/hirosebm10/
From the pictures it looks like that connect has roughly 30 pins. Good luck figuring out which does what. 
>> From the pictures it looks like that connect has roughly 30 pins. Good luck figuring out which does what. <<
Good luck, indeed. But . . .
I'm a newbie to the community, all right, and maybe a dreamer.
Yet, it seems to me with all the odd and weird displays from obsolete
and discarded media players, cell phones, and other gadgets . . .
that it might be nice to have a sort of database on these things.
When some smart fella here figures out the specs and connections on one of these, and especially if they figure out how to interface it to their Arduino
(hardware connections, drivers, and code), then into the database it
would go. Yeah, I'm a dreamer, all right.
The majority of displays used in phones, old PDAs, Laptops etc etc etc won't work with arduino because they need memory and driver circuitry that the Arduino doesn't have. Most of them are proprietary to the device, so even if they could be made to work, writing libraries is a huge amount of work that others probably couldn't use because the displays are too specific and its unlikely somebody else within the Arduino community would have one........
If you do a little research you'll find most of the displays that do work with Arduino are simple,decades old,generic and/or very common.
Nokia 3310 phone displays (anyone seen one of those in use since the 90's ?),the generic GLCD 128*64 and the almost prehistoric HD44780 text displays and most displays with a serial interface are safe bets for Arduino use........
This site has the pinout for an earlier iPod Video LCD:
http://www.electricstuff.co.uk/ipodlcd.html
Perhaps the pinout has been kept even though the connector has changed. The display apparently has memory so the interface is much like a memory chip: 16 bit bus, address strobe, data strobe, etc.