Morey's first patent, in 1793, was for a steam-powered spit, but he had grander plans. Morey realized that steam could be a power source in the 1780s, and he probably appreciated a steamboat’s potential from work on his father’s ferry and the locks he designed along the Connecticut river. In the early 1790s he fitted a paddle wheel and steam engine to a small boat and powered it up and down the Connecticut River. Legend has it, this was done on a Sunday morning, when the town was at church, to avoid ridicule if he failed.
The most important aspect of this craft was the paddle wheel. It was an old idea – supposedly dating to antiquities – and previously tried with a steam engine. Jonathan Hulls of England used a rear-mounted paddle wheel in 1737 but an inefficient method of turning the steam engine’s reciprocating motion into the circular motion hobbled it. In 1789, Nathan Reed of Massachusetts experimented with a paddle wheel, and considered patenting it, but eventually patented a different method instead. The American John Fitch experimented with side-mounted paddle wheels, but in 1791 used and patented oars instead. Morey's may have been the first successful use of a steam power paddle wheel, which was the best method of propulsion until the propeller, invented by Fitch, was perfected.
Morey’s first boat was little more than a proof of concept, so he built another in New York. In a letter to New York legislator William Duer, Morey describes how over the next three summers he traveled down to New York, and the following summer to Hartford, Connecticut to improve and exhibit his boat. Finally, in 1797 he went to Bordentown, New Jersey (a stop on Fitch's failed Philadelphia-to-Trenton passenger service), because it was “sickly in New York”, and built a boat employing two side-mounted paddle wheels. At this point, Morey considered his boat ready for commercial use and sought financial backers. For reasons that are unclear, his backing fell through because of “a series of misfortunes”. This is likely the end of Morey's direct work with steamboats – although there are many tales of a later fourth steamboat– but not the end of his steam engine patents. In addition to one received in 1795 for improvements he made working on the steam engine in boat, he received patents for other applications and improvements in 1799, 1800, and 1803.
Despite Morey's success in building a working steamboat, credit for the first successful steamboat line goes to Robert Fulton and his financier, Chancellor Robert Livingston. This was a cause for contention, as Morey claims that they took some of his ideas. His account, which seems more reasonable than later, derived accounts, is laid out in his letter to Duer and is as follows. The summer after the one Morey spent at Hartford, he returned to New York and gave Livingston a ride in his boat (perhaps at the advice of Benjamin Silliman — publisher of Morey's papers — who knew Livingston to be a supporter of the arts). He was impressed and offered Morey a “considerable sum” if he could improve the boat's speed to 8 miles per hour. He also offered $7, 000 for the rights to use his current work around New York but Morey declined the offer. However, he continued working towards Livingston’s speed goal. Morey had conversations with Fulton and Livingston, and Livingston even traveled to Orford to see him (although Morey doesn’t say when or what was discussed). Later, Morey reportedly was aboard Fulton's boat and expressed to Fulton his displeasure that his ideas had netted Fulton much but nothing for himself.