I'm going to really spell this out simply- you are probably not this much of a newbie, but I'm not 100% clear on what your problem is. Here goes:
So, you installed Linux on your computer. Then you deleted the partition. Using the live CD, you can run linux on your computer. Without the Live CD it doesn't work. Right?
Linux will run off the CD or the Hard Drive- except you broke the hard drive installation (don't panic, I'm sure we've all done that.
) So, I suggest reinstalling Linux.
If this isn't what your problem is, then please try adding some more details. Thanks.
Oh- sudo fdisk -l doesn't actually fix the problem- it is just a diagnostic. Tells us what is going on.