My iPod touch 1st generation won't connect to iTunes or YouTube.

Does it connect to the internet via Safari?

You say you have iOS 1.1.5. I would uopdate to the latest IOS for your model iPod. You get that here

Purchasing iOS 3.1 Software Update for iPod touch (1st generation)

I have a similar situation but with 2nd generation, and the updated iTunes. Any advice?

If you mean that when you connect the iPod to your computer it does not appear iniTunes then:

See

iOS: Device not recognized in iTunes for Windows

- I would start with

Removing and Reinstalling iTunes, QuickTime, and other software components for Windows XP

or

Removing and reinstalling iTunes and other software components for Windows Vista, Windows 7, or Windows 8

However, after your remove the Apple software components also remove the iCloud Control Panel via Windows Programs and Features app in the Window Control Panel. Then reinstall all the Apple software components

- New cable and different USB port

- Run this and see if the results help with determine the cause

iTunes for Windows: Device Sync Tests