Firstly, please say that you are doing this on a copy of the site, and not on the live one, or you made a backup site (or a backup of the files and the database)
Secondly, the difference between the version that you are too great… Maybe upgrade via Magento Connect is not the best way.
Anyway, since you have started via Magento Connect, lets continue that way. I recommend that if you have not made a backup, make one now. The best way is via SSH.
If you aready have a backup, ignore this.
To backup the files, simply compress them into a file, or even just coping the root folder of the site into another folder.
To backup the db, do the following linux command via SSH:
mysqldump -u [username] -p [databasename] > [filename].sql
Then it will ask for the password for the database user given in the command.
Now, lets try to fix our Magento Connect Problem
WARNING: THIS IS NOT GUARANTEED. Maybe you have another problem, or even upgrades from versions this old are not practical via this method.
After backed-up the site, still on the SSH, open the root folder of the magento installation and execute the following commands:
./pear mage-setup .
Make sure that you have typed the second dot at the end of the command.
While executing, there will be some messages. There should be no errors or warnings. After that, execute this other command:
./pear install magento-core/Mage_All_Latest
This one shall install all the core packages in their latest versions. If you are lucky, your Magento will work again. However, any hacks in the core files will be overwritten, so there might be some hard-working to put everything to work well again.
Best of luck!