without the lambda your fuelling will always be incorrect and you risk running lean enough to melt the pistons or rich enough to cause bore wash, take the exhaust to someone like longlife or powerflow they should be able to weld a lambda boss into your exhaust so that you can refit it, having it disconnected will not cause your car to not run, i would say you have disturbed something whilst removing the gearbox or battery check all your connections are on plus make sure you have fitted your earth lead back on the box if it had one fitted