There are a lot of people posting about the Illegal Disk problem without properly searching so please read this and possibly "Sticky" it.
100% Working Method
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Follow the instructions here to create a special DVD-Video formatted disc containing all your media files. This will read in any PS2 without the need for a modchip, because the PS2 natively reads DVD-Video discs.
http://sms.ps2-scene.org/SMSMANUAL/H...sage-dvdr.html
Swap Magic Method
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If you have Swap Magic then you can use it to make your data disc's read.
1) Boot SMS using whatever method you currently use.
2) Eject the drive and insert Swap Magic. (If you are using Swap Magic to boot SMS from a disc, then you must eject the SMS boot disc and reinsert the Swap Magic disc again)
3) Swap it with your data disc and the files should be visible in SMS.
Note: If you have the DVD version of Swap Magic then you can only use it to read DVD-R discs. If you want to read CD-R discs then you must use the CD version of Swap Magic.
SMS Boot + Data Disc
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Another method is to make every disc an SMS boot disc. Download one of the SMS boot disc images from the SMS site. Then use UltraISO to edit the ISO and insert your media files. Burn the ISO to disc and when you boot the PS2 with it, it will boot into SMS and already contain your media files.
***UPDATE***
Matrix Infinity / Modbo Workaround
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To get around the Auto-Sleep feature of these chips you can first insert your data disc into the PS2. Then POWER OFF the PS2. Then turn it on again with the disc already in the drive and boot SMS using Dev1 (Dev2 can't be used as it disabled the DVD Drive) and the disc will read.
Matrix Infinity / Modbo Permanent Fix
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The Matrix Infinity chips (and hence the Modbo clones) have an Auto-Sleep feature which turns off the modchip after the first disc has been "recognized" by the PS2 (in the case of games, once it has booted into the game)
Hence any disc that is inserted into the PS2 after this will not be recognized as it is not an original PS2 disc.
There is a wire labelled "RST" which connects the chip to the Reset/Eject section of the PS2 mainboard. If you disconnect this wire, then the modchip will be permanently active. Hence you can insert a disc at anytime and it will read.
However by doing this you lose the ability to disable the modchip by holding Start at boot time. If you hold the start button, it will still display the "Disabled" message, but when you press reset to restart the PS2, the modchip will still remain active and will boot backups. Hence if you play online, your modchip can be detected. There is also a possibility of "Anti-Mod" games detecting the chip and hence not being playable, but in all these years i have never encountered such a game.
I found this out experimenting with my modchip..If anyone else has any info about it then please post it here.
Note:
This doesnt seem to work on a Modbo 1.1 due to its different connections. (Thanks orangpelupa)
I have tested this on a Modbo 3.0 and it works.
BTW I have only tested this on a v4, v7 and v9. I don't know whether it will work with the slimlines.