So, the latest and the greatest VMWare Player (4.0.4) was installed.
Alas, it complains about services it needs to recompile, and that fails.
In detail, the virtual net services fail to compile.
Luckily, I found this blog entry.
Basically, download the patch mentioned, and execute
sudo su -
tar xvf /usr/lib/vmware/modules/source/vmnet.tar -C /tmp
cp /home/frank/Downloads/vmnet.diffs /tmp
patch -p0 < vmnet.diffs
cp /usr/lib/vmware/modules/source/vmnet.tar /usr/lib/vmware/modules/source/vmnet.tar.org
tar cvf /usr/lib/vmware/modules/source/vmnet.tar vmnet-only
Now, retry the compile by opening VMWare Player.
Even the networking part will now succeed and VMWare will present you a license agreement. You can now use VMWare player 4.0.4 on Precise Pangolin (12.04 LTS)