Starting a new game should not delete any previous save games (even uninstalling the game you should be asked if you want to remove the saves, or not). In any case, if you wish you can backup your existing saves first.
If you quicksave it will overwrite the earliest quicksave, but you can used named saves to make sure that doesn't happen. At least with the disk version you could edit a configuration file to increase the number of quicksaves kept (see the replies in
this topic).
Check your messages (click 'My Stuff' in the top menu bar, then 'My Messages').
