SeaMonkey is a browser but I see it also has it's own email client software. From what you say they are both combined into one application. Is that the case?
Tell us more about this performance loss.
What make and model computer?
How much RAM and how much hard drive space remaining?
Which anti-virus and is it a paid version of free? If paid, have you had to renew the license recently? (Some AVs cause problems when the license has expired and not been renewed).
What other security software do you use, eg Firewall, and do you use Spybot, AdAware, or Malwarebytes' Anti-malware or SPERAntispyware?
You said you tried to disable add-ons. Was this in Firefox, if so how did you do that? Did you try the Firefox button > Help > "Restart with disable Add-ons"?
Do you see this running slow with any other applications besides browsers?
Today, after running my antivirus, I first noticed that all my links in SeaMonkey 2.10, my default email client, would open up slow loading pages. Then, my Firefox 13.0 behaved slow while browsing, though both programs have reasonable start times. SeaMonkey is fine for viewing email as long as I do not browse. I had to use Task Manager to close them both. I am beginning to suspect some other underlying problem. These problems only occurred today but on this system, running Windows 7 Home Premium 64-bit Edition, they have both been reliable beforehand. Right now I had to use IE8 to post this message. I have tried to disable addons, but afterward both programs remain slow. Is there some issue with Mozilla; or is the problem somewhere else in my system?