Thank you, stsr505089, for figuring out an issue with a thickness of the hard drive.
I was replacing a dead hard drive in Dell Inspiron 1525 and fell with the same issue: for some reason BIOS does not recognize newer thin 7 mm hard drives so you have to get a thick 9.5 mm hard drive as a replacement. So i had to buy one more new hard drive that is 9.5 mm thick. Hopefully, now everything is up and running.
That's pretty odd.
When i inserted the first new hard drive that turned out to be a 7 mm in thickness, I checked how it's seated by unscrewing the small bottom cover (that gives you access to memory modules) - the hard drive contacts were inserted into the interface slot, but despite that it was not recognized by BIOS. So that really looks like there is some mechanical switch or something that prevents using thin hard drives. Pretty bizarre solution from Dell.