Are you talking about the "Swap Magic Boot Disc" ?
If so, I hate to tell you...... You are screwed.... There are quite a few games that these discs will not boot.... I have been seeing MORE & MORE posts about this same issue on other forums.....
Since you have the AR2... Try one of these and see if it will boot with your no-solder mod and the AR2 combo:
Booting a Playstation2 DVD (Silver or DVD-R) Gameshark 2 V1.99b and BELOW
• Boot GS2 disc 1.
• At the main screen, press the EJECT button to eject the CD tray.
• Replace the GS2 disc with an original PS2 DVD game, such as Devil May Cry.
• Close the CD tray (press EJECT again) and wait for about 30 seconds.
• Select START GAME and then select WITHOUT CODES.
• Once the GS2 is asking to change the game disc, press the EJECT button till the light changes from green to orange.
• The CD tray will now open and you can replace the DVD game with your backup copy.
• The CD tray will automatically close after about 5 seconds.
• Wait till the the power LED changes from orange to green again and press X now to start the game.
Booting a Playstation2 DVD (Silver or DVD-R) Gameshark 2 V2.01 and ABOVE
Thanks to Nighstalker for this method!
• Boot GS2 disc 1.
• At the main screen, press the EJECT button to eject the CD tray.
• Replace the GS2 disc with an original PS2 DVD game.
• Close the CD tray (press EJECT again) and wait for 15 seconds.
• Select gameshark codes and turn on or off any code on any game.
• Press start, select with codes and press x to load game.
• A black screen will appear saying "updating codes please wait"
• Do the R-mod swap by pressing and holding eject, swap with backup, tray will close and game will load.
• NOTE: The swap must be performed within the time you see the black screen.
• Nighstalker has tested this method with GS2 v 2.01 through 2.11.
• It works 100% of the time providing the backup is good.
Booting a Playstation2 CD (Silver or CD-R)
• Boot GS2 disc 1.
• At the main screen, select START GAME and then select WITHOUT CODES.
• Once the GS2 is asking to change the game disc, press the EJECT button till the light changes from green to orange.
• The CD tray will now open and you can replace the CD game with your backup copy.
• The CD tray will automatically close after about 5 seconds.
• Wait till the the power LED changes from orange to green again and press X now to start the game.
Booting a Playstation 1 CD (Silver or CD-R)
• Boot GS2 disc 2.
• At the main screen, select START GAME and then select WITHOUT CODES.
• Once the GS2 is asking to change the code archive, press the EJECT button till the light changes from green to orange.
• The CD tray will now open and you can replace the CD with your backup copy.
• The CD tray will automatically close after about 5 seconds.
• Wait till the the power LED changes from orange to green again and press X now to start the game.