A straightforward way to have Linux Mint 9 running off kernel 2.6.35 is by using the following method (based on my own configuration)
Open a Terminal and replace the Lucid repositories with Maverick repositories (Ubuntu 10.10 which is currently in development)
sudo gedit /etc/apt/sources.list
The default repositories list should look something like this
deb http://packages.linuxmint.com/ isadora main upstream import
deb http://archive.ubuntu.com/ubuntu/ lucid main restricted universe multiverse
deb http://archive.ubuntu.com/ubuntu/ lucid-updates main restricted universe multiverse
deb http://security.ubuntu.com/ubuntu/ lucid-security main restricted universe multiverse
deb http://archive.canonical.com/ubuntu/ lucid partner
deb http://packages.medibuntu.org/ lucid free non-free
Edit the list to look like this
deb http://packages.linuxmint.com/ isadora main upstream import
deb http://archive.ubuntu.com/ubuntu/ maverick main restricted universe multiverse
deb http://archive.ubuntu.com/ubuntu/ maverick-updates main restricted universe multiverse
deb http://security.ubuntu.com/ubuntu/ maverick-security main restricted universe multiverse
deb http://archive.canonical.com/ubuntu/ maverick partner
deb http://packages.medibuntu.org/ lucid free non-free
Save and Close
sudo apt-get update
Close the Terminal
Open up the Package Manager (Synaptic) and install/upgrade to the following packages
linux-firmware
linux-generic
linux-headers-2.6.35-6
linux-headers-2.6.35-6-generic
linux-headers-generic
linux-image-2.6.35-6-generic
linux-image-generic
linux-libc-dev
Once installed/upgraded close the Package Manager and Reboot
After you have Rebooted you need to edit the sources list again to bring them back to Lucid
sudo gedit /etc/apt/sources.list
deb http://packages.linuxmint.com/ isadora main upstream import
deb http://archive.ubuntu.com/ubuntu/ lucid main restricted universe multiverse
deb http://archive.ubuntu.com/ubuntu/ lucid-updates main restricted universe multiverse
deb http://security.ubuntu.com/ubuntu/ lucid-security main restricted universe multiverse
deb http://archive.canonical.com/ubuntu/ lucid partner
deb http://packages.medibuntu.org/ lucid free non-free
Save and Close
sudo apt-get update
Close the Terminal
Thats it kernel 2.6.35 is now successfully installed
Another worthwhile tweak if you have an Nvidia GeForce graphics card is to upgrade the driver to 256.35 (GeForce 6 and above)
HowTo install Nvidia 256.35 Drivers on Ubuntu 10.04/Linux Mint 9
http://www.webupd8.org/2010/06/how-to-install-nvidia-25635-display.html
also upgrade to Compiz 0.8.6
HowTo upgrade to Compiz 0.8.6 on Ubuntu 10.04/Linux Mint 9
http://www.webupd8.org/2010/06/upgrade-to-compiz-086-in-ubuntu-1004.html
LUg.