You may have to try one of the more manual removal methods since that OS X
version pre-dates a few better and available methods; however to identify the
item and then see what it takes to remove it from the suggested tested methods
is usually good for a start. Then try again if there are leftover unfinished parts...
•Adware Removal Guide -
http://www.thesafemac.com/arg/
Note: within the above, is this Identification page, that will help in manual removal:
http://www.thesafemac.com/arg-identification/ read through the page for best effect.
With an old browser, you may still be able to go into the Extensions (in Safari) to see
if any of the parts that affect the newer version are hiding there. You almost have to
go and install (by accident, or by bait-n-switch) to get several of the common ones.
More names of possible adware or malware items to look for in your browser extension
may include some shown in this Apple Support article, intended for later OS X + Safari:
•Remove unwanted adware that displays pop-up ads and graphics on your Mac - Apple Support
There is a chance your computer may have an older version of MacKeeper or some other
untoward badware that is counterproductive, slows the computer terribly, & adds no value;
if so then the means to remove it may vary. I've no experience in those; and have avoided
the temptation to click on any "free download" cleanmymac, mackeeper, or other garbage.
Of course, it would usually go without saying "do not download or install their offer, do not
call any toll-free number (that may not be one) nor accept offers, scams, to fix your Mac!"
Later, you may be able to find a less unsecure browser, to try. The better choice would
require your computer to be running Tiger 10.4.11 or 10.5.8; that's TenFourFox browser.
http://www.floodgap.com/software/tenfourfox/ - has info, it's not for 10.3.9 though.
Hopefully this helps. It takes time.
Good luck & happy computing! 🙂