Hewlett Packard does not officially support the HP Color LaserJet 2800-Series (including HP Color LaserJet 2820 and HP Color LaserJet 2840) on Windows 7 32/64-bit. However, I’ve found a blog entry describing the installation process using some workaround.
In short, the author downloaded the HP Toolbox for Windows Vista, unpacked it and turned on the Compatability Mode (click right, choose Properties) for the following files (change for all users): setup.exe, Hpzstub.exe, hpzsetup.exe, hpzice.exe, autorun.exe.
After that, you can install the HP Toolbox by running the setup.exe (it may seem that the installer doesn’t continue in the middle of the process – be patient). After rebooting, change the permissions of C:Program FilesHPToolbox (or whereever you installed the Toolbox) so that LOCAL SERVICE, NETWORK SERVICE, and Users have full permissions. Reboot again – printing and Toolbox should be working now.
According to the author, scanning should be working as well. For me, it didn’t. You may have more luck.
Further information, hints, and guides on how to configure your firewall can be found here: http://www.weston-fl.com/blog/?p=439