Hello, macboyme
Consider the following in any order you find relevant for your system:
(0) You write that you are using a 4pin to 8pin adapter. However, I think you mean 6pin to 9pin adapter.
External iSight is a Firewire device that uses a 6pin Firewire 400 connector.
Newer Macs have only 9pin Firewire 800 connectors, so it is common to use 6pin to 9pin adapters similar to the one I normally use:
http://eshop.macsales.com/item/Newer%20Technology/FIR1369AD/
The only 8 pin cables and adapters I could find were USB. They won't work on Firewire devices.
4pin Firewire is a mini connection that I have only seen in cameras. If you really are using a 4 and/or 8 pin cable, I suggest you try a different Firewire adapter method.
My suggestions below are based on using a 6pin to 9pin adapter like that mentioned above or cable like this one I have also successfully used:
http://store.apple.com/us/product/TP320LL/A
(1) Test in another User Account on your iMac. Be sure to also consider all the other suggestions for external iSight from:
http://support.apple.com/kb/HT2090
You do not say which of your Macs has only FW800 ports that require a Firewire adapter. To remove as many variables as possible, test the same cables and Firewire 400-800 adapter on both Macs if it is possible to do so. If you only use the adapter on one Mac, it is possible that the adapter is the cause of your trouble. If one of your Macs has only FW400 and the other has only FW800, test with a different adapter or use a 6pin-9pin cable to test both your Firewire iSight.
Also, test another Firewire 400 device to eliminate the possibility that your problem is caused by one of your connections.
(2) For additional ideas on how to test external iSight, consider the additional suggestions here:
http://www.ralphjohns.co.uk/EZJim/EZJimpage4.html
Unless the software and connected peripherals are EXACTLY the same on both your iMac and your MacBook, be sure to consider possible hardware or software conflicts with something else installed in or connected to your iMac. A link to more info about conflicts is included in the "How to test..." page.
(3) If you can rule out both possible conflicts and connection problems in the iMac, the problem must be either in your iMac's user account or in the system software used to operate your external iSight.
You can rule out problems with the user account by testing in several different accounts.
If the problem is EXACTLY the same in any user account you test on your iMac, your system software is suspect. Backup all your important files, repair permissions, and apply the 10.6.4 Combo Update:
http://support.apple.com/kb/DL1048
Follow the restart that completes the Combo Update with another permissions repair. Then test iSight again.
(4) Once your external iSight works correctly with your iMac's QuickTimeX, iChat, etc., it will work as well with Flash video websites as it does when you are running it from your MacBook.
EZ Jim
Mac Pro Quad Core (Early 2009) 2.93Ghz w/Mac OS X (10.6.4) MacBook Pro (13 inch, Mid 2009) 2.26GHz (10.6.4)
LED Cinema Display G4 PowerBook 1.67GHz (10.4.11) iBookSE 366MHz (10.3.9) External iSight