I read the installation instructions that came with the DVD box. They said to insert the DVD into the Mac and run the installer. I did so but the Leopard disc never appeared on my Mac desktop. Also the Mac became very, very slow.
I spent the better part of an hour trying to launch System Monitor and Terminal and Console to try to find out why the Mac was crawling along and why the Leopard disc was not mounted. I also launched Disk Utility, which never appeared either.
After watching a spinning beach-ball for almost an hour, I powered off the Mac and restarted. It spit out the Leopard disc and it was working perfectly, no slowness anywhere. The only hint to the problems was in system.log where something complained about timeout in connecting systemuiserverd. (I cannot find that anywhere now, apparently the Leopard install somehow lost yesterday's syslog.)
I plugged in a USB keyboard and mouse and booted from Panther installation disc, ran Disk Utility and did Repair Disk and Repair Permissions. There were some incorrect permissions in some files relating to iso9660 filesystem.
Reboot. Insert Leopard disc. This time it mounted. Run Leopard installer. It rebooted from the disc. The Microsoft USB mouse did not work in the installer, but the installer was fully operational with the keyboard. I chose default installation, which upgrades an existing OS X to Leopard. It told me it will take more than 3 hours to finish installation. I went to bed.
In the morning I was greeted by the OS X login window and hidden behind it was a window that asked what kind of keyboard I was using. Unfortunately I was unable to bring that window to the front because the Microsoft mouse was still not working. But the Mac was now up and running, so I turned on my bluetooth mouse. It worked, I managed to get the Mac recognize my keyboard and logged in.
The first thing that popped up was a window that asked me which wireless network I wanted to connect to but there were no wireless networks available. In reality my Linksys AP was on and working. I had no time to debug it any further at that time, so I shut down the Mac.
The next time I booted the Mac, the Microsoft mouse worked! And when I logged in, I was presented with a list of all wireless networks. I connected to my WPA-protected wlan with no problems.
I haven't booted the Mac since and I haven't had any other problems so far.