I have two small 12v power bricks, one of them a 3-prong 1.5A SMPS and the other a 2-prong 1A linear power supply. I don't know exactly what is inside the SMPS because it just came with an old modem, however I do know that the linear one is just a transformer attached to four diodes and a large capacitor. Can I just wire the positive SMPS to the negative linear to get a 24V power supply, or would that mess with the SMPS?
If one of the supplies is 2-prong then it’s not earthed and so you can connect them in series. The other one may or may not have its negative output connected to earth. The voltage output will be the sum of the two and the current capability will be the lower of the two, being 1A.