Laptop or phone don't recognize connection

I had the same issue, however what I DID notice up on top was a USB Connected - the USB icon. I pulled that notification up and it asked me to connect. The exacts are:

1. Plug the USB cable into the computer
2. Plug the USB cable into the phone
3. The notification up top corner left will say "USB Connected" with a USB notification icon - BRIEFLY. The text "USB Connected" will quickly disappear, but the icon is still in the left corner.
4. Pull down the notification andyou'll see "USB Connected - Select to copy files to/from your computer" - Select that notification
5. Notification "USB Connected - You have connected your phone to your computer via USB. Select "Mount" if you want to copy files between your computer and your phone's SD Card." - Select the option "Mount".
6. The "Removable Disk" notification should pop up asking you what you want to do. I select "Open folder to view files".

There is a music folder in there, or whatever else you'd like.

Hope that assists.

There may be a physical issue with your logic board. You can get the part at HTC G1 Repair and there is a guide that shows you how to put in the part at HTC Repair Guide.