Like I said, I don't think xbox 360 modchips exist. At least not like original xbox modchips that allow you to play back-ups.
The way it works for the 360 is that you open the 360 and remove the dvd drive. You then connect the dvd drive to your PC through a SATA cable. One end of the SATA cable connects to the 360 dvd drive and the other end connects to a SATA port on your motherboard. If your motherboard doesn't have a SATA port, you can get a SATA card to connect to one of your PC's IDE connections, then connect the other end of the cable to that SATA card.
From there you run a simple program from your PC and it will backup and flash you 360's dvd drive. You then detach the 360's dvd drive from the PC and reinstall it back into the 360.
All of that will allow you to play your back-ups from the 360's dvd drive which you just flashed the new firmware to.
Pretty easy. No?
Since you have a Toshiba-Samsung, it is relatively easy. Your next step, if you wished to persue this, would be to open the case and determine what version your 360's drive is.
Opening the case:
http://www.informit.com/articles/art...&seqNum=2&rl=1
To determind what version drive you have you need to open the case and look at the top of the dvd drive. It should say somewhere on there
F/W: MSxx (xx=25/28). Either MS25 or MS28. If I remember correctly, The MS25 is the easiest to work with. The MS28 requires a few extra steps when it comes to flashing the drive.