AFAIK the TOGA switches are inhibited on ground after landing to prevent mistakenly pressing one if you're fumbling for the reverse levers etc.
For the take off roll pressing the TOGA switch will give you the rated thrust selected during the performance figure calculations in the FMC. Once airborne pressing the TOGA switches once will give you HDG REF as a roll mode and TOGA for the thrust ref with an appropriate thrust to give you a climb rate of 2000fpm.
A second press of the TOGA switches will give you max rated available thrust.
Pushing the thrust levers fully forward will give you max available engine thrust.