How big (approx) is your database if you know. Can you run a repair and optimize on your database tables for us? (Admin > Utilities > SQL Manager).
1) “Decompresson Failed”
Are you getting this message after you’ve downloaded the archive? Could you try alternating between zip and gzip and see if one gives you better results? Also, do you have access to another archive program? On windows, 7zip is good. If you’re on a Mac let me know and I’ll pull up some alternatives for you there (although the default archiver on my Mac has always worked for me).
2) How do I get a valid database backup.
Your host probably has PHPmyAdmin available to you. What many users do is simply use it. You will find that as the database gets bigger and bigger, it is more reliable.
Finally, what version and build of EE are you running?