For ShippDriver:
The machine has an ECS mobo, but I can't seem to download a manual from their website to check details. However, what you need normally is in BIOS Setup, often the the Advanced Peripherals section, called something like Boot Priority Sequence. It is not in the Windows boot menu system.
To get into BIOS Setup you usually hold down the "Del" key when you turn on the machine. Before starting this, I suggest you DISconnect the old drive and get it set up with only the new 1 TB unit installed. Then we'll add the other back in. So, disconnect old 500 GB unit, close the case, hold down "Del" and turn on. In Integrated Peripherals check that only one device shows up on a SATA port and check its mode - may be IDE (or PATA) Emulation, or may be native SATA, maybe even AHCI. Whatever that is, remember for use later. Back out of there and go into Advanced Peripherals or wherever the Boot Priority is set. Since you have no optical drive in right now, ensure this is set to boot from the 1 TB drive that is there and nothing else. Save and Exit to boot that way.
Now that you have the machine running, find the website of the manufacturer of your old failed 500 GB HDD. Look there for a free downloadable set of disk testing utilities. For example, Seagate has Seatools, WD has Data Lifegard. If you can, I suggest you download the version that is "for DOS" or something like that. This is a version you burn to a CD or DVD. Then you boot from it and it installs its own mini-DOS so you can run diagnostics without having Windows running.
Shut down, and re-install the optical DVD unit. Reboot and use the diagnostics utility package to burn the software onto a DVD disk. Reboot while holding down the "Del" key and this time go to Boot Priority and set it to boot from the DVD drive first, then the 1 TB unit. Save and Exit with the new utility disk in the DVD drive, and it should boot from that DVD into the mini-DOS, giving you access to all its tests. Now you can try out some tests on the 1 TB unit although you don't have any need to test it. This is just a brief "get familiar with how it is supposed to work".
When that's done, shut down, disconnect the 1 TB unit and connect in its place the 500 GB unit. Close up, hold down "Del" and turn on. Go into Integrated Peripherals and look for that drive on the SATA port. Make its mode is the same as the before. Back out and go to Boot Priority, and check that it shows the old 500 GB unit as the second device to try after the DVD drive. Save and Exit. This should boot cleanly, from the DVD again, and this time you can run all the tests on the old drive to find out what it has trouble with.
IF the disk is judged usable, and if there's a routine to surface-test the entire disk, run that - BUT it will take many hours. This routine will force the disk to check itself and find any questionable sectors. Any that are found will be replaced with a spare good sector the disk has hidden away, and if at all possible it will move data from a questionable sector to its good replacement while the old sector is still readable. This is a different type of job than the Surface Test that ScanDisk does and it will make fixing other problems a bit easier.
So, now you have info on what hardware difficulty the disk has. If it really is unreadable you may have to give up on it or contemplate spending much money on professional data recovery. On the other hand, if it has few or no hardware problems, you may be able to recover data from it simply with a copy operation. Worst case, it may have data corruption that requires using software utilities by yourself to recover Partitions, recover the data in a Partition, or both.
So, assuming you decide to try copying from it, shut down the machine. Disconnect the DVD drive, move the data cable for the old 500 GB to the second SATA port, and reconnect the 1 TB new unit to the first SATA port. Close up and boot into BIOS Setup. Make sure both drives show up as SATA devices in the right mode. Then check Boot Priority and make it use the new 1TB unit ONLY - no other choices in the list. Save and Exit, and it should boot cleanly into Windows from that new disk, unless somehow your system is set up to insist on trying every device it has. This should (I hope!) get you into Windows cleanly where you can examine both disks. You can go about the process of trying to copy all files from old to new unit right away. Or you could try running Scandisk on the old drive to see if it will fix some remaining problems. On the other hand, if it cannot show you the drive or all its files, let us know what you do get. Maybe we can suggest next steps if you tell us what happens all the way through this list of steps, especially what the disk diagnostics tests tell you.