Laptop Backup questions and Concerns

I have an Asus laptop that I bought last year. It had Windows 7 on it and I upgraded it to Windows 8 when it came out. I would like to back up the entire drive, including the hidden partitions because I would like to set up Linux on it, and the last time I did that, I borked the entire setup and I had to restore it from scratch. This time, I have a means to back up the system whereas before I didn't.

Now, complicating matters is that when I attempt to do this, I get an error in ATI2013 warning me that the "1" partition cannot be read due to an error. I presume the "1" partition is the one that has the GPT information. Similarly over the past couple weeks, I've also been getting nastygrams from Windows claiming that my hard drive has a problem.

My question is this: Since I will be forced to take the unit in for service under warranty, can I get away with just backing the C: partition and the separate Data partition (D:) so that if any data is lost during the repair, I can simply reinstall ATI2013 and copy them back to the new drive and pick up where I left off before? I have already had to deal with one total system loss, and I would like to avoid a second one, if possible...