WiFi Problems on iTouch 2nd Gen
This is relatively common for that generation (and 3rd generation). Typically, when the Wi-Fi goes out, the bluetooth will as well since they're on the same chip. Is that grayed out as well? If not, it can still be the Wi-Fi chip. 

There's not really an easy fix for it. It's definitely going to be a swap out, especially with your volume button issue. You can take your iPod to the Apple Store and they'll give you a quote on a replacement. It'll probably be around $99. 

Something else you could try is restoring your iPod Touch in iTunes. Make sure you set it up as a new device.