I have installed Flash but it doesn't work and there's no note about it in the about:plugins page in Firefox. Here's my proof:
I'm on Ubuntu 8.04.
Recommend going to Karmic anyway.
Help us a little here to help you...
Give us the results of these commands (the results shown are as on my Karmic system)
Run synaptic and select the flash plugin you installed to see what files it actually put where.
Ah! I see you got the .deb from Adobe. Hmm. No telling off hand what silly thing they may do... anyhoo, all the more important to find out where they put what, because unless that matches with where your firefox is Bad Things (like it not working) will happen.
I found this little script from Internet which fix this problem always.