Can my G5 hard drive be installed in a powermac G4 tower?

Your iMac G5 has an 80 GB SATA (Serial ATA) hard drive, which isn't compatible with the onboard IDE buses in the G4s. You could install a Sonnet SATA controller PCI card like this one in your G4, which enables connected drives to be bootable. Keep in mind that you could buy a factory-refurbished Western Digital 250 GB IDE hard drive for less than the cost of that SATA PCI card. To use the small (by today's standards) 80 GB drive, you'll spend more than it's worth.

Note, the only way to ensure it is bootable is an erase and install of known compatible installers for the G4. A Firewire SATA case can also be used with the same limitations on booting. PCI Powermac G4s, the first ones from 1999, do not support Firewire booting. Pre-867 Mhz G4s do not support 10.5 without a special software known as LeopardAssist, and this includes the dual 800 Mhz G4s. You need a G4 with no Firewire 800 to support 9 booting.

Not knowing where you're located, I'd recommend that you check computer retailers in your area or online. You'll need an enclosure that's internally designed to accommodate a 3.5" SATA hard drive and that has external FireWire ports on the exterior. Depending on the enclosure chosen, it will also include an external power supply or (if a larger enclosure) it may only need a standard computer power cord. From past experience, Forum regulars would suggest that an enclosure with an Oxford chipset on the enclosure's bridge board would be more Mac-compatible and trouble-free.

You were able to select the G4's hard drive while booted from the OS X installer disk and then used Disk Utility to erase it - correct? Did you reformat the drive as an HFS+ (Mac OS Extended) volume? After you locate a suitable FireWire enclosure, compare the price to a factory-refurbished IDE hard drive. I bought a Western Digital factory recertified 250 GB IDE hard drive for less than $50 (USD) about a year ago. WD thoroughly tests them and then applies a new label to the drives indicating "recertified." I wouldn't recommend buying a used hard drive that's "refurbished" by some third-party entity, unless the seller's return policy is good. A hard drive can be perfectly functional, yet have noisy (worn) motor bearings.

The computer was able to boot from the installation CD, but couldn't find a HD to install onto.

Typically this means you need to format the hd. Or, could be a bad hd.

Format a disk using the installation DVD

To format the startup drive, you will need to run disk utility from your installation DVD.

This article will tell you how to get to disk utility. Once in a disk utility, you can go and format the disk.

http://support.apple.com/kb/TS1417

To format your startup drive, you will need to run disk utility from your startup DVD.
Mac OS X 10.4: About the utilities available on the Mac OS X 10.4 Install DVD

http://support.apple.com/kb/HT2055

How to run disk utility from your startup DVD.

1. Insert your startup DVD into your reader. Power down your machine. Hold down to the c key. Power on your machine. This will bootup your startup DVD. ( Alternatively, you may hold down the control key, this brings up the startup manager. Click on the desired volume. Click on the right arrow. )
2. This will bring you to a panel asking you for your language. Pick your language.
3. 
   
4. You you come to the Install Mac OS panel. Do not install.
5. Click on Utilities menu item. This will give you a pulldown list of utilities.
   
6. Click on the disk utility.

7. Start up disk utility.
   On the left pane view, you will see a list of all your disks. Click on the external disk.
   Click on the partition tab.

   

   
   

8. You will now see how your external disk is currently set up. Fill in the information as appropriate. You should pick Mac OS Extended (Journaled).

More details on formatting.
http://www.kenstone.net/fcp_homepage/partitioning_tiger.html