Yes if you have another drive that is at least the size of you data ( So if you have a 500 GB but only 200 GB used you can use a 250/320 if you want) I use Marcirum Reflect which will allow you do clone to a smaller drive as long as its bigger than the amount of data you have. Now when you first install it it will ask to create a Rescue Media. You want to do this. It will download some stuff that is needed to make it (It will delete it when its done). Then burn it to a disk. Then turn off the PC, Plug in the drive you wish to clone to and unplug all other drives (Just leave the source and destination drive) and of course your DVD Drive. Then Boot from the CD. Once booted click on the Disk Image tab at the top, select your Source drive (Current one and make sure its the right one! Maybe before you boot from the drive, boot with the extra drive and delete the partitions in Disk Management so you can tell the difference) and click the Clone this Disk below it. Then select the other drive and start the cloning process. Once done, Turn off, Remove CD and Backup Drive, connect other drives and boot back up!
Now as far as the 4TB drive goes i don't your motherboard will have an issue. I have a ASUS P5N-D which is also a 775 socket CPU with an NVidia 750i Chipset and it reads my Seagate 4TB fine on the motherboard SATA ports.
If it can't you could find a cheap SATA III Controller that you can toss in your motherboard and connect it to that and that should read it just fine.