I'm working on this linux server and so I needed to set a path for bash so that I could use this program. I modified the bashrc file by adding two lines of code....

g03root="/share/apps"
Export PATH$:g03root/g03/bsd/g03.profile

or something to that extent. Anyways, I didn't know what I was doing and now I can't use programs such as vi and such since it is an unrecognized command. I wanted to change shells to fix bashrc, but I can't even do that it seems. What should I do?

Depends on the distribution but the usual way to add to your existing path is:
PATH=$PATH:/my/path/foo
export PATH

You can execute vi via its absolute path i.e
/usr/bin/vi