Can I start with a new Library folder?

I dont see why you shouldnt be able to start over with a fresh library. Any application that access files in the library will create new paths and files that are needed. You will need to set up all your applications and personal settings again. I'd recommend just moving the files out of your library as opposed to deleting them altogether, since you may need something and will be able to restore things if there's a problem.

First off Leopard won't let you get rid of the Library or change it you also cannot remove the folders inside of the library or change their name. You can however remove the contents of the folders in the library.

As far as doing doing harm, yes down right removing the library will do harm, not to your pictures or your music, personal documents however it holds all your preferences, the data in iCal, address-book, mail, bookmarks, user specific widgets and that is just a start of the Apple programs built into the OS and doesn't touch on 3rd party applications.

So I advise to start in the ~/library/preferences folder, look for toast preferences, then proceed to other preferences. But don't delete them move them to the desktop then log out or restart and test.

You can also try removing the caches folder in the library (you can trash it).

However unless you are comfortable with using the root user or terminal I would advise backing up your data and migrating to a new user. Because without root or terminal doing anything but the preferences folder gets tedious.