Windows – OS reads only 1600GB of the 4TB hard drive

It looks like something has trashed your GPT data -- both the main data structures and the backup data structures. I don't know specifically what might have done this, but a buggy partitioning tool seems like the most likely culprit. Another possibility is that there's been some confusion over something like a RAID configuration -- if the disk was originally prepared with your motherboard's RAID features active and then accessed with the RAID features inactive, something like this might have happened.

Two options seem most reasonable at this point:

1. Re-create your partition "blind." The vast majority of modern partitioning tools begin partitions at sector 2048, so you could use gdisk to create a partition that begins at that point and that ends at the last possible sector. This stands a good chance of succeeding, but there's a risk that if your original partition did not start at sector 2048, you could end up damaging it when you try to access the new partition. Also, some tools will try to create a new filesystem when you create a new partition, so using them would be risky at best. (I recommended gdisk for this task because it does not touch the partitions' contents, just the partition table that defines them.) Also, if the disk held an EFI System Partition in addition to the main data partition, the main data partition would not begin at sector 2048.
2. Use a tool like TestDisk (included on many Linux emergency systems, such as PartedMagic and System Rescue CD) to search for your missing partition. (There are Windows equivalents to TestDisk, but I don't know what they are, offhand. You could do a Web search to find them, if you prefer to work from Windows rather than boot a Linux emergency disc.) This will be more likely to find your partition if it was placed strangely, but tools like this can become confused if the disk has been re-partitioned in the past -- they can sometimes detect the remnants of deleted partitions and try to re-create them even though they're no longer valid.

Take your pick as to the approach, and good luck! Whatever you do, though, be cautious. You might consider doing a raw disk backup to a spare disk, if you've got one that's big enough to hold all your data. If you do this, though, be very careful in specifying the source and destination disks, or your backup could end up trashing the data you intend to save!

Well, first, I don't think that's a good idea to have such a big OS partition anyway. A much smaller SSD for the system and the big HDD for other things would be much better.

Anyway, to answer your question:

First check if your mobo supports UEFI booting. If it does, then it is possible, but not through 'simple' meanings.

You can try to burn a DVD and install from there.

If all the above fails, read this. If still doesn't work, also see this page and scroll down till you reach the 'Windows' section. It talks about boot-loaders and such.