Here is how I installed Linux Mint Menu in Ubuntu 9.04 Jaunty Jackalope. I downloaded the following packages from the Linux Mint Repo which can be found here:
mintinstall
mint-info
mintsystem
mintmenu
These are the packages (current versions at the time of writing, I recommend you download them from the repository than from these links):
http://packages.linuxmint.com/pool/main/m/mintinstall/mintinstall_6.3.7_all.deb
http://packages.linuxmint.com/pool/main/m/mintsystem/mintsystem_7.5.2_all.deb
http://packages.linuxmint.com/pool/main/m/mintmenu/mintmenu_4.7.9_all.deb
For my 64-bit version (amd64), the mint-info package is:
http://packages.linuxmint.com/pool/romeo/m/mint-info-x64/mint-info-x64_7.0.1_all.deb
For 32-bit, it may be different. Try:
http://packages.linuxmint.com/pool/main/m/mint-info-universal/mint-info-universal_7.0.1_all.deb
Now, install one by one in the following order:
mintsystem
mint-info
mintinstall
mintmenu
After the installation is done, right click on the panel and select Add to Panel. Then find mintmenu and add. To change the icon, right click on the menu and click on Preferences and then in the Button Icon, put in the full path to custom icon. You may want to put in /usr/share/icons/Human/22×22/places/start-here.png
Please share your results.