Boot won't complete

Aspire X3960
For the last 2 months I have been unable to get into the OS.
I can get into BIOS no problem.

I have tried switching ports, plugging in a new hard drive, reinserting all of the cords, moving around the RAM, removing and reinserting the graphics card.
I have also tried loading defaults on the BIOS.

There is 1 of 4 things that will happen;
1. It will start up "normally" but after ACER screen it sits for a while with a blinking cursor before turning off.
2. It will start up into the troubleshooting mode, with which I have tried to boot into safe mode and recover it, to which it freezes and reboots.
3. It will start to automatically repair the drive, however the furthest it has gotten is 57% before it freezes and reboots.
4. It does not even begin turning on, just lets out a constant beep that doesn't stop, ie. no breaks or patterns, just a non-stop beep. It does not reboot from this, it has stayed like this for >8 hours before.

Some info that hopefully will help;
BIOS Version is P01-A4
i7-2600 CPU @ 3.40 GHz
8GB RAM
Running Windows 10, ran this for > 1 year, before this it was Windows 7 Premium 64 Bit
AMD Radeon HD 6570

I would very much like to preserve my files.

Accepted answers

All comments

IronFly

one thing you can try is to create a bootable windows 10 USB media, boot from it and check if you are able to recover some files from your HDD.
or installing a fresh copy of windows 10 in a new HDD and then plug your old HDD and recover your files.

1) download a windows 10 iso using Microsof tool:

http://go.microsoft.com/fwlink/?LinkId=691209

select the proper windows 10 version (the same installed on your laptop) and choose to save it as iso file when prompted

2) download Rufus:

http://rufus.akeo.ie/?locale=en_US

plug your USB flash drive, run Rufus then:

select ISO image from the dropdown menu near "Create a bootable disk"

click on the little icon on the right and browse to the windows 10 downloaded iso file

as Partitions scheme select "MBR partition scheme for BIOS or UEFI"

as File system select "FAT32"

click on Start

wait until it finish, then uplug your USB flash drive

3) Reboot to BIOS, pressing F2 at boot if it's a laptop or Del key if it's a desktop, then press F9 to load default and F10 to save and exit

4) plug your USB flash drive and at boot press F12 (if F12 doesn't work, see if it auto-recognise the USB flash drive or press F2 or Del key to enter BIOS and enable F12 boot menu under BOOT tab), choose the USB flash drive as bootable device

here you can continue to install on your new HDD or

you can try to backup your files using this trick from windows 10 installation media:

https://www.howtogeek.com/135005/how-to-use-a-windows-installer-disc-to-back-up-your-files-when-your-computer-wont-boot/

Tugvow

2) download Rufus:
as File system select "FAT32"

Thanks for the reply IronFly. I am up to this step but Rufus will not allow me to change the file system to FAT32, it only has NTFS, after following all of the prior steps.
Will this work anyway?

IronFly

Try NTFS but normally FAT32 is the standard.

Tugvow

I've thing I did notice was that during the set up for the windows creation tool, the was an option to create it as a USB rather than an ISO ope what the instructions you posted said. Might this be a better option to ensure it to allow fat 32