The only way to upgrade 10.4.x (tiger) was to purchase the 10.5.x (Leopard) upgrade.
So if you are confidant you were using 10.5, you would have had the disk to do the upgrade. The last version of Leopard was 10.5.8 which would have allowed you to run iTunes 10.0 and also run Firefox. Unless you used Time Machine to back up your computer or can find the 10.5 disk, there is no other way to get 10.5 back on the system.
If you attempted to download 10.6 (Snow Leopard) it was nothing but an update, the update would not run in 10.4.
Before buying a 10.6 install disk, be certain your computer meets the specifications required by Snow Leopard. System requires to install Snow Leopard are linked below and also on the right side of the page has information about what is needed to upgrade 10.4 to 10.6.
While Apple has updates at their website, they do NOT have a full functioning operating system for download nor do they have downloads that will change the OS from Tiger to Leopard or Leopard to Snow Leopard. Upgrades of Mac operating systems need to be purchased while updates can be downloaded. See the second link for Apple's explanation of the differences.
I recommend, if you pursue purchasing and installing 10.6, that you completely erase the drive before running the install. Disk utility is used and accessed through the install disk when it's booted from and than the drive can be erased. Once the drive is erased the Mac operating system can be installed. Be certain to find how to install the operating system before you begin. You will loose whatever data is on the drive.
PS Here are two links so you can see what the boxes look like for 10.4 and 10.5:
1) Mac OS 10.4 : http://www.amazon.com/Apple-Mac-10-4-Tiger-VERSION/dp/B0002G71T0/ref=sr_1_1?ie=UTF8&s=software&qid=1305175757&sr=8-1
2) Mac OS 10.5: http://www.amazon.com/Mac-OS-Version-10-5-6-Leopard/dp/B000FK88JK/ref=sr_1_1?ie=UTF8&s=software&qid=1305175907&sr=1-1
------EDIT------
I need to clarify my comment "there is no way to get 10.5.8 back on the system. Actually, there is, you can spend around $169.00 at Amazon and purchase the Leopard install disk. I figured though if you could upgraded to Snow Leopard that the $29.00 expenditure at Apple would be preferred to the $169.00 expenditure at Amazon.