First read through, I failed to notice where we switched from a Windows 8 Dell to a Vista Sony!
Getting back to the OP's Dell, it would look like the HDD might be the most likely culprit but equally, it could be some other component timing out or even a memory error that is constantly correcting.
You say that it won't now boot to safe mode, which eliminates most of the software issues, since safe mode is not trying to load a whole raft of drivers. Did you try debug mode in the boot type menu? Logically, that shouldn't work either but I did have a laptop one time where that was the ONLY mode that would boot - but it never flagged an error!
Clearly, though, the first thing you must do is try to get the files you need off the hard disk and so you need to boot something. In such cases where the primary system won't boot, I've used a couple of live CD tools - if you don't have a CD, you can use a USB stick instead.
One tool is Knoppix, a live CD version of Linux, specifically for diagnostic work. Don't worry, it comes up to a GUI and there should be an icon for your hard drive, which you can click on and work down the directory tree to the files you want and copy them to another external drive. A couple of cautions, my version is old, 10 years maybe version 3.4, newer versions may behave differently and Knoppix comes from Germany, so when it boots, you need to specify lang=us in the options. Yes, it can read NTFS files,
The other tool is the bootable CD version of Partition Wizard. It uses a Linux base but you never see it. Once booted, it will show you all the partitions on your hard disk. Two tools can be useful, one is a disk check utility from one of the top menu dropdowns (varies by release). That would confirm the condition of your disk, which may suggest an approach. It's other tool is a disk copy (i.e. clone) to another drive, so if you have multiple partitions, it may be able to copy some of them to an external HDD. Note that it will need as much space on the clone as the original and the space must be unallocated and unformatted. Be VERY careful with this program, it will attempt to do whatever you tell it, so be extremely careful not to specify your system disk as output!!!
if you can get your system to boot to Windows, you might want to try a small utility called Testdisk (Google it), which has a plethora of disk management software in it but I think it's only for Windows.