This will get the job done:
You have to be able to access the files on the server where the site is.
Judging from your source code it looks like you need to look on the server, in the folder /Portals/0/Skins/Skins/
In there you will find several files ending in .ascx
If you do not know which one of those is being used as the basis of your portal skin then go and look at your Admin, Skins page and see if the filename shows there as your selected skin.
Open that ascx file in your editor (Frontpage, Notepad or whatever) and look in the top few dozen lines for a section/tag beginning: <dnn:SOLPARTMENU... etc.
Cut and paste that section from <dnn through to /> into another notepad file for safekeeping. Or just delete it if you have a backup of this file.
It also looks like you should remove the two class statements that create that orange bit on the menu:
class="MenuBG" and class="MenuRight"
These should both be very near each other. Just cut the statements as they are out of the code.
Save the file back on the server to the right place and force-refresh your site (CTRL -F5).
I've made this all up from a glance at your source, so I could be wrong somewhere.
Good luck,
Rob