Q: imap server password authenication failure

I have a stand alone mac with MAC 0S X Version 10.7.5, and also iPhone and iPad.  recently i signed up for a google account on my iPad. but when i opened up the   mail icon on my main computer  an error message came up  - " mail was unable to log into the IMAP server  "IMAP.gmail.com" using password authentication - verify account settings - log into web browser http://support.google.com/mail/accounts/bin/answer.py?answer=78754 (failure).   I tried this but had no success. so  I removed the account from my mail  and then tried to reinstate the original gmail account also without success.  mail is coming into my iPad and iPhone without me signing into google.  if i connect my iPad to my main computer will this do the trick and restore the gmail account ?