EMB-170 Captain reported a go-around was initiated but TOGA did not respond resulted in an unstable approach.

Narrative

On final approach in ZZZ; I was the pilot flying. I turned off the autopilot around 500 feet. The approach was stable. I had ice speeds; which brought my Vap (Approach Speed) to 148. I caught a gust as I was passing the airport perimeter road which caused me to balloon. I counteracted the balloon and remained stable. I passed the threshold at approximately 70 feet. I was somewhere between 0-20 feet and I was floating down the runway. I called for a go-around because I was going to be outside the touchdown zone and pressed TOGA. The throttles did not advance and we did not get TOGA thrust. Simultaneously we touch down on the runway outside of the touchdown zone. We had plenty of remaining runway and we were below 100 knots. As we were pulling off the runway; we noticed we had GA (Go Around) on the PFD (Primary Flight Display) but no crossbars. We also got the EICAS message ENG TLA (Thrust Lever Angle) NOT TOGA. I called Maintenance to see if anything had to be written up for the throttles not advancing. He said no and transferred me to Person A who said I should write this report.