It's not strange at all really, for the IIsi anyway. Now that you've all but eliminated the adapter as the problem, it's time to check out the monitor you're using. From your description, it sounds like your monitor is getting a signal, but it can't sync to it. Is that what you mean by "the monitor turns on?"
It's my guess that you're using an LCD that requires a 60Hz signal, not a MultiSync. But if it is, you probably need to use the adapter settings for 13"/14" RGB to get it to work if you haven't tried that yet. I've got a 17" Sony Trinitron and Liberty Adapter combo that has displayed just about anything I've ever thrown at it, but that's the only setting it will Sync to from the IIsi. The 12" RGB setting gives an out of range error and both LC settings result in a couple of barely audible clicks, but not even the sync range error. The Portrait setting, the IIsi's only usable output for a graphics production or word processing environment as far as I'm concerned, works with my silver bullet combo after a fashion . . .
. . . but a wide and squat, dim, incredibly cobalt blue image on the trusty Trinitron isn't what I'd describe as particularly WYSYWYG!
) When Apple hobbled the IIsi, they well and truly borked the maximum memory allotment and its vampire video subsystem's output both.