Ok.. for starters.. throw away that two wire cord and get a proper 3 wire grounded plug. Mains driven devices are not to be trifled with in regards to proper wiring. Just cut the end off a PC power cord, if your like most, you probably have a few laying around.
On your laser PS, Hot is brown, neutral is white, green is ground.
On your 3 wire cord, you can have two possible wiring colors used. IEC or US National.
If it's IEC, hot = brown, neutral = blue, ground - green/yellow stripe
If it's US National, Hot will be black, neutral = white, ground = green
Just match up the hot, neutral and ground to their respective colors. and it should work... and for safety's sake.. don't just 'twist the wires together'. At minimum use electrical tape and tape them up. This hobby isn't worth someone getting electrocuted over.
My guess is currently, you have the hot/neutral reversed and/or the PSU has a safety that won't let it operate without a ground.