YOU CANīT COPY FMCB!
It must be installed (or at least, you need a way to get the MCID of your MC, which involves starting Homebrew in a way...).
Please post the Model-Number of both of your PS2.
The NoMod-PS2 is a 10000. o.k.
What kind of model is the chipped PS2?
If I remember correctly, the 10000-Models have a third exploit (not the PS1-Exploit and not the FMCB-"Softmod"...), which you maybe can start with also.
Do you have an Original NTSC-J PS1-Game (for exploiting your unmodded PS2 with the PS1-Exploit)?
The PS1-Exploit CAN be copied to another MC, but it is still Region-Specific.
Means, you can copy the TITLE.DB "per hand" to your MC and exploit a Target-FAT-PS2 simply this way, but you need to copy it in a Region-Specific folder (B?DATA-SYSTEM, where "?" is the region-specific letter.) + you need to edit the TITLE.DB to match the SLES/SLUS/..., which is different from game to game and even between games from region to region.
You need a PS1-Game, which is running on your FAT-10k-PS2.
This games SLUS/SLES/...-ID you use, to create a TITLE.DB.
PS2 V7/DMS3 V2 (FW:2.4b7); Seagate Baracuda 200GB
PS2 V7/CC1.0 (FW:34 hacked v2 BM:2.1.6); Maxtor DiamondMAX9 PLUS 160GB
PS2 SCPH-30004R; NoMod+NoLaser
3xSony MC 8MB
MAX/Datel 16MB with Boot-CD
Custom FMCB 1.8b+ Beta-Build, my AIO 0.5, Sony&xRhino-Linux