mIRC v6.35 works fine with Windows 7, I cannot think of any reason why it would run and then suddenly disappear when you try to join a channel.

Are you using any scripts or addons?

Are you using anti-virus/firewall software? That might be the cause of the issue since some of them sometimes incorrectly think mIRC is a trojan/virus and may delete and/or terminate mIRC without telling you.

The warning from Windows 7 about Microsoft Agent support is a known issue (it is in fact a Windows 7 issue) and has no effect on the way mIRC works.