Currently, I have on the C:\ (Primary Partition) Windows Vista Home Edition. A few months ago I partitioned the hard drive to have ~130 GB for whatever (Logical Drive E:\; D:\ is 10 GB used for backup) so that I could dual boot. The E:\ has Windows Vista Business (64-bit).

Is it possible to format the C:\ while booted in Business and then merge two two partitions so that only one OS exists on one partition?

Depends on if that is your "System/Boot" partition?

The C:\ is the system boot partition.

I re read your post and you have logical drives assigned to the other two, I don't think you can boot to a logical drive.

Your best bet would be to use Acronis or similiar program to image your partition containing the OS you want to keep over to an external hard drive or cd/DVD that is after you copy bootmgr and Boot folder to the OS you want to keep also. Then wipe out all your partitions and re create what ever you want. IMO do not create any logical drives unless you just absolutely have to.
Then use the Acronis to transfer the image to your new partitions c:/ reboot to your Vista DVD and do a startup repair.

in any case you will loose boot {mbr} loader which is installed on C:/ partition. you have to save your datas on another driver and start all over again with partitioning