Have you run Activity Monitor in Utilities to see if there is any indication of what may be holding things up? Do you run a lot of apps at the same time, have a bunch of apps/plug ins open on start up?
As you mentioned, an SSD would dramatically improve things, but there is a possibility that you have some bad blocks in your HD, causing some glitches. A lot of bad blocks will eventually prevent the imac from mounting the HD at all. You can run an Apple Hardware Test on start up to see if it finds any hardware issues. Hold down D on start up to launch this. Here is a link on this-
https://support.apple.com/en-ca/HT201257
In my experience though, a slow performing mac comes back to the HD being a SATA and not SSD. Are you running Yosemite? I am guessing the iMac came with 10.8? I know a lot of people are eager to upgrade their OS as soon as the new one comes out, but performance will always be best when you leave your machine on the OS it shipped with- unless it has an SSD/Flash Storage and some decent RAM