Okay here is what I did...
First you have to install checkgmail from repos (even though it won't work yet). Then...
1) the file checkgmail no longer works with google's new software, but I found a corrected file in Germany.
I have uploaded it for you here: https://backup.filesanywhere.com/FS/v.a ... 6772ac73a3
2) download the new checkgmail file and (as root) replace the one in /usr/bin (you MUST take ownership of the file)
and give [yourself and root] priveleges to read and write, and make sure you check the box to make it executable.
3) in mintmenu find Startup Applications and make a new entry, make sure you enter this under command: checkgmail --no_cookies
4) restart and when checkgmail opens enter your info and password and wave file if you want a sound and icons you prefer.
the command to play a wav file when you get mail is: aplay /home/Music/whatever.wav (assuming you have aplay installed)
That's it, enjoy!