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You need free space on a hard drive before you can add partitions.
The only way to remove an OS from your old HD is to delete or format the partition.
What size are your external storage devices?
How much used and free space is there on the old 500GB HD?
It is best to keep your OS (and programs) in a separate partition, this will make it easier to re-install, repair or move the OS, and make backups.
Since your WD 640GB 7200RPM 32MB cache, has a better sized cache, than the Seagate 500GB 7200RPM 16MB cache. I'll assume you want the OS on the WD.
With your old HD still plugged in, install the new WD 640GB HD, initialize and partition it.
First primary partition should be the OS, 60 - 80 GB is recommended. If you are installing a lot of software and games make it a little bigger.
Most people put their programs in the same partition as the OS. Some people put their programs in a separate partition.
If your programs and OS are in the same partition, then use the above size for the first partition.
If you plan on putting the programs in a different partition then you can make the OS partition smaller, 40-50GB, check your programs sizes make the second partition with enough room to add more programs in the future.
For this scenario I'll assume you are going to put the OS and programs in the same partition.
Second Partition for personal data and should be a Logical partition. You will have to decide what size you need.
You can add a third and forth if you want to keep Videos, Music and anything else in a the data partition or in a separate partition.
After all partitions are made, shutdown computer, unplug the old HD, re-start the computer, select boot option key and boot to DVD or installation device.
Install Win7 on your New HD first primary partition.
After installation is complete, shutdown your computer and plug in the old HD, start computer. Go to BIOS and set new HD first in the boot order. Save and continue booting.
Move the data you want to the new HD.
If you want to leave the old OS on the old HD, then your done.
If you want to delete the old OS and use the space, then you will have to move all the data you want to save from the old HD to the new HD.
Format the old HD.
Setup any partitions you want, move any data you want back to the old HD for storage.
If you are going to use Windows disk management for partitioning the new HD, have a look at these tutorials.
Partition or Volume - Create New
Partition or Volume - Delete
For backups or cloning you can use Acronis True Image as mentioned earlier or you can get a free version of Acronis from both WD and Seagate.
Seagate DiscWizard
Western Digital,
Acronis True Image WD Edition.
Other free backup programs:
Macrium Reflect
Paragon offers
Drive Backup for free.