Can't re-install homebrew
Short term answer, try this command to see if your brew installation worked:

/usr/local/bin/brew doctor


It seems that your bash environment may not be looking in the /usr/local/bin for executibles (which means you have to write the full path rather than just the name of the command). The solution may be just resourcing your conf files, which can be roughly done by closing your terminal and opening a new one. Otherwise, you'll want to add a line to your ~/.bash_profile. I think resourcing will do the trick though.

So after confirming the success with the first doctor, try quitting your terminal application and starting fresh, then your original usage of brew should work. If it doesn't try:

echo $PATH


and report  back the results.