Your G4 may not be fast enough or have enough memory for a standard Leopard install. These issues are easy to overcome. I have Leopard on a 733 MHz G4+ which does not meet Apple's requirements - it works exceptionally well. Original Leopard install DVDs were double layer and this alone can make installation tedious on Macs without an optical drive which can read them.
Which model G4 do you have?
Below you will find my standard OS install advice.
It is always best to have a full bootable backup before you upgrade. If you fail to do this you will be unable to return to this OS if you decide you don't like the new OS. Also there is a slight chance that an install could lose everything on the Mac. The backup must be to an external hard disk. Preferably use Carbon Copy Cloner to make a bootable backup of the whole disk.
Erase before the install
Once you have a bootable backup on an external disk it is best to erase the internal disk with the new installer DVD before you install.
During the install
Preferably do not import any data or preferences from earlier OSs during the install process as this can reintroduce bugs.
OS numbers and names
OS X 10.4.x - Tiger
OS X 10.5.x - Leopard
OS X 10.6.x - Snow Leopard
OS X 10.7.x - Lion
OS X 10.8.x - Mountain Lion
More about Macs
The Apple History site has specifications for every Mac ever produced: http://www.apple-history.com/
Upgrade to Leopard
Those wishing to upgrade to Leopard should be aware that install disks can be expensive unless you contact Apple. Details: http://lowendmac.com/deals/best-os-x-leopard-prices.html Standard Leopard installers impose several hardware limitations including speed and RAM size but all these restrictions can be overcome. Google for details. Leopard works well at 500 MHz with 1 GB of RAM and many happy users have less than this.
Upgrade beyond Leopard
OSs beyond OS X 10.5.8 require an Intel processor. If in doubt check this: Click the apple at the top left of your screen and select 'About this Mac'. This will give you your OS number. Then click 'More Info' to see which processor you have. If it says PowerPC you cannot upgrade to Snow Leopard and above. If you have an Intel Mac it is well worth upgrading to Snow Leopard now and then considering other options after that. You can buy Snow Leopard here: http://store.apple.com/us/product/MC573Z/A
Upgrade beyond Snow Leopard
Information about upgrading Snow Leopard to Lion or Mountain Lion: http://store.apple.com/us/product/MD256Z/A
Check that your Mac complies with any requirements. If you are not in the US you should use the Change Country link at the bottom of Apple pages.
It is a power Mac g4 350mhz family number M5183
Runs windows xp virtually one 30gb hd and one 40gb hd
I recently put in a io magic idvd168dl
It does not boot to anything but the 30gb hd if I try a gray screen
Comes up then a blinking happy Mac to question mark
For 2min then boots to the 30gb hd.
Your G4 is too slow to accept a standard Leopard install DVD - this can be overcome in various ways - Google for tips.
Does your G4 meet the Tiger requirements at the following link?
If it meets the requirements you could reset PRAM as the following link describes and try again:
Install CDs or DVDs must either be the grey ones originally shipped with this model or be the black general purpose 'retail' versions - I don't know why they are called 'retail' as the same ones are used for wholesale customers.
It is possible your optical drive is not bootable. That isn't too unusual with third party optical drives for which the real driver support isn't there until the system is fully booted. Support is not there when you first startup and the system is not yet running. Some drives (such as Pioneer, but probably others too) do have this pre-system support and can be used as replacements for the Apple original. Check www.mac-sales.com and see which models they sell. If you just replaced the drive for the DVD support but still have the old one and it works you can put it back in for OS installation purposes. I keep my old drives for that purpose though I have been fortunate in that the ones I have put in to replace them seem bootable (the one time I needed to do that in the past 7 years).
Also note as Neville Hillyer observed that your computer is significantly below specifications for OS 10.5 The workarounds mentioned might get it on there but were really intended for people running machines that were just below the 867 MHz set by Apple, not less than half that which your Mac runs. That is just the processor speed requirements and we know nothing about your RAM.
In the past Pioneer drives have been a safe bet (e.g., from [OWC|http://eshop.macsales.com/item/Pioneer/DVR116DBK/] or [Newegg|http://www.newegg.com/Product/Product.aspx?Item=N82E16827129023]). However, check [Jeff's January 2010 post about re-branded Pioneer drives|http://discussions.apple.com/message.jspa?messageID=10839236#10839236] that are no longer really Pioneer manufactured.
[Power Mac G4 (Digital Audio/Gigabit Ethernet): Replacing CD/DVD Drive|http://docs.info.apple.com/article.html?artnum=58698] (text only)