On my old computer I installed PostgreSQL on my external hard drive. Now I have a new computer, but the same external hard drive. What do I have to do to "install" PostgreSQL onto the new computer so that the databases remain intact?

depends how you installed postgresql on the external drive... the whole thing, just the $pg_data or even just a tablespace?

I installed the whole thing on the external.

then really all you need do is create the limited user account "postgres" on the new machine, and start the server as that user - not that I know how to do that on windows, nor add the startup command to autorun as a service I think you can see the startup / shutdown commands by looking at the start menu shortcuts on a system where postgresql is installed already.

do you remember what version you installed? if so, I'd likely just install it to the same location on the external HDD (and untcheck the option to "initiate the database cluster") - that will take care of account / service creation I believe, and it should just start using the existing $pg_data folder.

i'd probably copy/paste the whole folder / rename from the external drive, just in case something goes horribly wrong

Running the installer without the "initiate the database cluster" worked. It actually checked if the folder was empty and asked me if I was sure, when I wasn't paying enough attention and tried to hit next when it was checked.