iPhone 3GS will not connect to iTunes

Have you followed the instructions in the error message and restored the phone?

If you can't update or restore your iPhone or iPod touch - Apple Support

You might also want to consider that it's time to get a new phone.

I can’t read your computer screen; it’s too small and sideways. But you do realize that the 3G networks that the 3GS requires will be shut down by almost all carriers within the next few months, so it will be useless as a phone?

Jc-iPhone wrote:

I got it from ebay

Regardless of where you got it from, it's essentially obsolete.