Hello, & a warm welcome! 🙂
You can keep eMail in the iCloud even in 10.5.8.
Good work so far, if you now wish to upgrade we just need to make sure the Disk is OK & that your Mac can do it.
Could be many things, we should start with this...
"Try Disk Utility
1. Insert the Mac OS X Install disc, then restart the computer while holding the C key.
2. When your computer finishes starting up from the disc, choose Disk Utility from the Installer menu at the top of the screen. (In Mac OS X 10.4 or later, you must select your language first.)
Important: Do not click Continue in the first screen of the Installer. If you do, you must restart from the disc again to access Disk Utility.
3. Click the First Aid tab.
4. Select your Mac OS X volume.
5. Click Repair. Disk Utility checks and repairs the disk."
http://docs.info.apple.com/article.html?artnum=106214
Then try a Safe Boot, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, reboot when it completes.
(Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive.)
Snow Leopard/10.6.x Requirements...
General requirements
* Mac computer with an Intel processor
* 1GB of memory (I say 4GB at least, more if you can afford it)
* 5GB of available disk space (I say 30GB at least)
* DVD drive for installation
* Some features require a compatible Internet service provider; fees may apply.
* Some features require Apple’s MobileMe service; fees and terms apply.
Which apps work with Mac OS X 10.6?...
http://snowleopard.wikidot.com/