Failed Hard drive, Replace with temp hard drive, now missing pci root express drivers

SO a couple weeks ago, my pc was running really slow out of the blue, so i decided to run a diagnostics test through the BIOS, everythings fine, except for the hard drive, my laptop starts ringing and beepeing super loud, so i force shut it off, i reboot it only, to now have no OS....So i salvage a hard drive from another dell laptop, it took a mintue but i have windows 10 pro 32 bit on it, originally, my laptop was 64 bit,with windows 8 on it . but now i have done all the little system updates along with driver updates, i goto device manager and in other devices theres 4 unknown, and its the pci root express, i have searched 6 different hells for it and have come up with nothing, is there a solution to that? or is it just saying that? also, is there anyway i can save my orginal hard drive? i have a SATA cord and it pulls up most the data, it just gets slower everytime i try to explore the hard drive