Teamcity agent service on EC2 not connecting

I have a teamcity cloud server. And also I have a AWS account with a Windows EC2 inctance. I logged in to my Windows EC2 inctance and set the Teamcity Agent through web UI downloading Windows installer and with the option "Service". When I look at the services on my windows EC2 instance, I see that TCBuildAgent is running as a service. When I look at the cloud teamcity account, I can see my EC2 instance trying to connect. I authorized it. But it stays in disconnected state even though my EC2 instance is there open. What am I doing wrong? This I get if I try to run Agent Start command: 

Starting TeamCity Build Agent Launcher...
Agent home directory is C:\BuildAgent
[2025-01-26 15:57:11,679]   WARN -      jetbrains.buildServer.VCS - '[C:\BuildAgent\temp] hg version --quiet' command failed.
[2025-01-26 15:58:40,970]   WARN - buildServer.AGENT.registration - Error while asking server for the communication protocols via URL https://erginegider.teamcity.com:8111/app/agents/protocols. Will try later: java.net.ConnectException: Connection timed out: no further information (enable debug to see stacktrace)
[2025-01-26 15:58:40,970]   WARN - buildServer.AGENT.registration - Error registering on the server via URL https://erginegider.teamcity.com:8111. Will continue repeating connection attempts. 

Eventually I need to start this EC2 automatically with teamcity build start. But I can not even get a connection state. Please help.