R-Drive Image should recognize and work with an external USB2.0 hard drive. If it doesn't, contact our technical support and provide them the model of your external HDD. They will help you with this problem.
If you can get inside your system and have enough experience with the hardware, the best way to transfer your logical disk C and other partitions is to connect your new hard drive to another IDE port, start your system up in the Windows mode, and copy the old HDD to the new one. Before your start, read R-Drive Image help carefully (Disk Actions -> Copy a Disk to a Disk -> To copy data from an entire hard drive to another hard drive:). Then turn your computer off and replace the old HDD with the new one. That should work.