A G4 QS 2002 model has a max OS version of OS X 10.4 (Tiger).
It originally came with OS 9.2.2 and some version of OS X from10.1.2 through 10.2 (which specific version depended upon when in the production period it was shipped).
Leopard and later can not be installed on it. Reason - Leopard and later require an Intel processor.
OS 9 (any version) can not be updated to any version of OS X. OS X is designed to install alongside any existing verion of OS 9 already present; the two OS's are intended to cohabit on those machines which can use both (in OS 9's case, as an OS or as Classic). No OS X installer will run while the machine is booted to OS 9.
What you probably downloaded from CNet is an OS X upgrade version. Those upgrades require that the machine already be booted to an earlier version of OS X of the same base version (i.e., an upgrade to 10.4.11 would require the machine be booted to some earlier version of OS X 10.4).
There are no free full install versions of OS X legally available, other than the public beta OS X 10.0 and some 10.1 disks released as promos. All subsequent versions require an original OEM disk set (the one that came with a machine and usable only on that specific model) or a retail disk set. Once that version has been installed, it can be updated to the max point version for that base version using download updaters.
There are no download updaters available to take an OS X install from one base version (such as 10.3 Panther) to another base version (such as 10.4 Tiger); such a jump require the use of a retail disk set. This means that if your goal is to have Tiger on the machine, there is no point in acquiring/installing any earlier version. Get the retail set for Tiger and install it.
Your best option is to acquire a retail disk set for Tiger (or earlier version, if that's your final goal).
Such can be purchased from places like HardcoreMac, but prices there are pretty steep.
You can usually find better prices at places like EBay or LEM Swap, but be sure what is sold is what you really want.
Friends and Apple User Groups are other possible sources.