Dreaming slightly! Haha.. Though, it may be possible to attach the HDD as external and transfer your saves/progress (you'd need to ask for help transferring Trophies etc) you could always back up vital stuff to a USB drive...if you ever get it to boot..crap.. Hmm.. Shame there's no way for me to get physical access to it, otherwise i could help far more easily
And good idea with the whole Gaming PC.. They are a bit more useful. Yes they can cost a lot if you go OTT, but my last gaming rig besides like, two little upgrades, lasted me a good 7-8 years before it felt like time for a new setup.. I skipped pretty much all the i7 CPUs from 2nd gen and went all the way to 8th.. Plus i just loved the Coffee Lake codename xD coffee! <3 haha. You don't have to go as OTT as i did, though i'd recommend spending as much as you can and avoid AMD unless you want to heat up your room a little and have higher energy bills, though they do still give a cheap bang for the buck, Intel stuff is generally more reliable and efficient.. Not -always- the case but usually. My old machine case in point, kept up with mid-end newer gen i5 machines at the core!
But coming back to your PS3, i'm fairly sure it's been stated that each HDD is semi 'locked' to each machine once formatted, so even if the HDD worked in your other system you'd lose access to some things unless you edit a certain file, except if you've never been on PSN and it's all 0s.. Again, you'll have to ask the others about that, i don't want to end up helping destroy any vital data that remains. Did you see what error you got on boot without a HDD, btw? Also, i need to read the first part again but have you actually got the PS3 to do the whole filesystem check, much like an early PC used to?
And thanks for what? Nothing is working yet! xD Besides, you can find HDDs cheap now.. 500GB drive for like, £10 on eBay, maybe 15 bucks? So, if the console is working, upgrading the drive could be one way to at least have some good come out of this lol