Since we don't know all the steps you too, if you would indulge me...
You did not tell us which Macintosh you are using - or which version operating system (though I am guessing Mac OSX) - or what, exactly you are expecting to happen that you defined as "it did not recognize it on my computer"...
Also, I presume by "ilink to firewire cable", you mean a 4-pin to 6-pin firewire cable to connect your camcorder's DV port to the Mac's firewire port. (USB will not work and USB-tofirewire cable/converter/adapter/hub things won't work, either.)
1) Mac is on, at a stable desktop.
2) Camcorder is off and not plugged into the Mac with the firewire cable.
3) Plug the cable into the camcorder's DV port. Plug the other end of the firewire cable into the Mac's firewire port. You should probably plug the camcorder's AC adapter into a known working AC outlet and the camcorder's power port.
4) Power up the camcorder - the Power button allows you to select the mode for the camera - either "Camera" (to record images through the cameras lens) or "Play/Edit" (to play back video captured on the tape). The camcorder must be in "Play/Edit" mode.
5) Launch iMovie. A window that allows you to name the iMovie project, select the destination of the video project file and select whether DV or DV widescreen (among a few others). Select whatever format you recorded to the tape - most likely DV. Create.
6) The iMovie blue import project window should appear indicating "Camera connected". Using the camera or iMovie camera controls, rewind the tape if needed - then Import.
So... what happens when you go through this?
I have an old sony handicam DCR-TRV17 and I am trying to transfer the mini DV tapes it records to onto my computer. First, I got an ilink to firewire cable and plugged that in but it did not recognize it on my computer. I got the software disk for the camera and tried to open MGI Videowave III which is on the disk, but it says "You cannot open because the Classic environment is no longer supported." So, I was wondering if there were any other software programs that would work with this camera so that I could transfer my videos?