when I measure Amps directly from the power supply, I get 0 amps regardless of anything being connected. If I have the fan connected and spinning and try to measure the Amps, the fan dies until I stop trying to measure (but I measure around ~3A).
What is the power rating of the peltier. If it draws in excess of the power supply rating, the power supply's protection circuit will be cutting off the output (crowbar protection) and won't reset until you remove the load. Typically a 50mm square peltier will pull 5 amps at 12 volts, so at 19 volts you could be talking about 7.5A which exceeds the PSU rating.
It's a bit like beer drinking.If you have a barrel of beer and you know that you go bonkers after only 2 pints, you'll still try and get four or five down your gullet.