As you don't give any model indication, except for "older Dell Inspirion", it's hard to tell. I have been using Knoppix 6.X on several machines fitting that description, all the way back to i8100, with no problem at all.
You might try with an older Knoppix, like 6.0.X.
I doubt there is really a problem with text-only mode, as it seems that you have been able to enter init cheat codes. As you know which graphics module is used, you could check out hints for that. I have saved the day that way.
Somehow, I feel that you haven't gone thoroughly through the whole list?
Code:
knoppix screen=1280x1024 Use specified Screen resolution for X
knoppix hsync=95 Use 95 kHz horizontal X refresh rate
knoppix vsync=60 Use 60 Hz vertical refresh rate for X
knoppix xmodule=ati|fbdev|intel|mga Use specified Xorg-Module (1)
knoppix xmodule=nv|radeon|savage|s3 Use specified Xorg-Module (2)
knoppix xmodule=vesa|svga|vmware Use specified Xorg-Module (3)
knoppix norandr Disable Xorg RandR feature (may be
useful if wrong resolution was detected)
knoppix noddc Don't query monitor for resoution
knoppix no3d|nocomposite Don't use Xorg Composite extension
knoppix vga=normal No-framebuffer mode, but X
knoppix nodrm Don't load graphics acceleration modules
knoppix nofb Don't load framebuffer modules
knoppix nomodeset Don't use Kernel Mode Settings for X
fb1280x1024 Use fixed framebuffer graphics (1)
fb1024x768 Use fixed framebuffer graphics (2)
fb800x600 Use fixed framebuffer graphics (3)
fb640x480 Use fixed framebuffer graphics (4)