OK. This helps a little, though yes, this doesn’t indicate whether 4.1.9 was installed. But the serial would indicate your Cube was built at the end of 2000. The 4.1.9 updater was released early/mid 2001.
So… the first thing I would try to do is download the G4 Cube’s 4.1.9 firmware updater and follow the instructions on installing it. If it was previously updated by a previous owner, then the firmware updater should display confirmation of this and end the installation process before it would proceed. It would not need to be run a second time. [UPDATE: Yes, your Cube is updated with 4.1.9f1, according to the last section]
The next thing I would try is to burn the
CD installation version of Tiger, instead of the DVD images. At the time, Apple released a special order version of Tiger on CDs, for the few models which could install Tiger but lacked a DVD-ROM drive or SuperDrive.
Specifically, grab
downloads #26 through #29 from the Macintoshgarden and burn these to CD-Rs (not DVD-Rs).
When you’re ready to install, put in CD #1. When you restart, hold down the
Option key until a screen comes up, showing the icons for all of the hard drives and optical discs which are bootable. In your case, you should see both your OS 9 drive and the CD icon with CD #1 of the 4-disc Tiger CD install. Wait for the pointer to appear and then click to select the CD.
Let us know how it goes!