A -1 error can also be because your device is flashed onto an unofficial baseband firmware (iPad Baseband in the case of the 3GS), and because it's not official, Apple does not recognize it and sees it as a hardware issue. Not saying that it's not possibly a hardware issue, but just putting it out there.
To see if you're actually having a hardware issue, you'd most likely need to create a custom IPSW to preserve your baseband to bypass Apple's check on your current firmwares.
Download RedSn0w 0.9.15 beta 3 for
Windows or
Mac depending on computer OS.
Download the 6.1.6 IPSW for the iPhone 3GS
here.
Then run RedSn0w as an administrator (if applicable). Click on Extras -> Custom IPSW, and your file browser should crop up. Browse to the 6.1.6 IPSW that you just downloaded, and let RedSn0w do its thing. Afterwards, click on "Pwned DFU" that should be on the same screen where you clicked "Custom IPSW". If you don't see it, close out RedSn0w, re-open, click on Extras -> Pwned DFU.
Follow the instructions on screen (it may take a few times to get it right) so that you get your device into a black screen with no backlighting. Open up iTunes once again, and hold Shift (Windows) or Command (Mac) and click on the Restore button that you've clicked on to get the error message in your provided screenshot.
Your file browser should open once more. This time, point iTunes to the IPSW that you just made.
NOT the one that you've downloaded, the one that was made using RedSn0w to preserve the baseband firmware.
Let iTunes do its thing. If you still get error -1, you have a hardware issue, but because it's a 3GS, I'd place my bet on having an iPad Baseband on your device, which is why you're getting the -1 error.