old iPod touch 1.1.4 youtube app hasn't worked since Sept 2011 or so
Actually I suspect your problem started when the YouTube API 1.0 was dropped by google.

Google notified developers that the YouTube API was deprecated in 2008. Since they keep deprecated APIs running for 3 years, 2011 would be the time they turned the switch on it. It would make sense if all apps and webpages relying on the YouTube API v1.0 failed when they shut it down. They had a lot of problems with YouTube in september 2011 (example with 502 errors). So it's reasonable to say that your iPod will never be able to connect to YouTube if you keep using the early 2008 iPhone OS 1.1.4.

Google released the YouTube Data API (v2.0) around march 2008, after the iOS 1.1.4 was released.

I fear the only solution to get your 1.1.4 device to play YouTube properly would be to get Google to turn the old API back on... Or simply update your iPod :(