Stupid Question - Downloading Captivate to New Device - Where is it?

I had the same problem and was asked to download the trial version even though I have a subscription.

Then it kept asking for a serial number which there isnt one.

Then I had to get an Adobe rep on chat to figure out what was going wrong-  30 minutes and some directory renaming later they got it working. Not as easy as it should be. 

You didn't mention which version you were using, nor if it is a susbcription or perpetual license.

Adobe policy has changed since a while. You will only be able to download the two most recent versions, which means 10.0.1.299 fro CP2017 or 11.5.1.499 for CP2019. There is NO easy way anymore to download older versions. If you have a version older than CP2017 you will need to contact Adobe directly.

Captivate has never been part of the Creative Cloud app family.  Getting hold of a download file for a recent older version is usually still possible, but be warned that making sure it is compatible with your current Operating System is super important.

Which version of Captivate were you using on your old computer?  If you have a subscription, does this mean you were on Captivate 2019?  If so, you should be able to just download the current Trial version of Captivate 2019 and make sure you are logged in with your subscription Adobe ID.