Laptop?
memory is adequate, processor is adequate.
initramfs is definitely a RAMdisk creation routine. and the fedora erros comes before at boot I am pretty sure this is the same issue (no Ramdisk no place to extract kernel files for boot)
I've read some linux forums where the best guess is a bad cd/dvd reader, but no proof that is the issue. Keep trying you might want to search on google for RAMdisk issues installing or booting linux though.
I did find this: "If you have Windows already installed on your machine, you might also try making a boot floppy. There should be utilities on your CD f/DVDor doing this. Boot your PC from the floppy, and then tell it to do a CD install."

I noticed you mentioned you only had 70MB of disk space? This really shouldn't affect the boot up as with a clean install you have 0 disk space but if you get far enough you'll need to blow off the other partitions in order to install a functioning desktop installation.

When you do just let the install setup your partitions getting into partitioning HDs for different uses can get complicated and even contentious. most distros give you an OK setup for a decent desktop most the distros use package managers and they install to system default locations; it's best to let use their recommended layout. far out of the norm