what they didn't steal or conquer was developed by a warrior-scientist caste
Klingons developed technology the same way every society and race, learning about things over time. One must remember that it has only been in relatively recent times that the Klingon Warrior caste has wielded absolute power over the empire. Look at the scientists and researchers involved in the augment virus crisis, it's clear that the Klingons have and do engage in the same kinds of research and development other species do. As a related note it is likely that some of the technological advances they have came from other races but what exactly those technologies are is unknown. What we do know is that the Klingons seem to have amazing insight into the creation of cloaking devices, so much so that it is thought that the Romulans in fact acquired what they knew about cloaking from previous Klingon designs.
I'd always wondered how the Klingons got off the ground, in fact they traded the cloak with the Romulans as per TOS I believe. Once they had that I suppose anything else is pretty plausable, but before that you'd have to assume that some advanced race had the misfortune to encounter the Klingons, most likely crashing upon Kronos. They would have had to learn the rudiments of space-faring from these people as well. Another likely factor in the Klingon desire to leave the planet would be that according to legend, Kahles told the Klingons to look for him on a planet surrounding a distant star. Eventually they founded the Monastary that Worf would eventually attend in his search for spiritual fulfillment.