MacBook – Compatibility of Mid 2011 MacBook Air 13″ Parts

Likely to be the adaptor cable if it's cheap - might not be able to handle the HD throughput (although outputting to HDMI, you'd think it'd be able to).

While this sounds counter-intuitive, try moving around the alignment of the second screen as this might ditch the 'snow'.

Also, have you tried the screen with any other HD inputs?

You'll have a much better vantage point than us on the internet to guess.

First, reconnect all cables and hope it's that.

If not, you'll need to start replacing parts one by one. The odds of a new LCD being faulty are low - but the circumstances of the repair might help.

Was the LCD out the reason you swapped the panel?

You might need a second machine to isolate each part - test whether it's the cable, inverter, logic board LCD or something else.