I will now try to install tiny core again, using the manual you provided ( http://wiki.tinycorelinux.net/wiki:installing_tc_-_alternate_offline_guide ). Is this any different to the manual on http://distro.ibiblio.org/tinycorelinux/install.html ?
The finished installation should be the same.
This is written for those who don't have an appropriate internet connection to be used during installation.
It also explains things in a different way. If there is something you don't understand on one page, see the other.
I suggest using an even easier way.
Download and use tinycore_3.6rc3. People reading this in the future, should use the latest version. This is the latest version at the time of writing.
Use HD/USB Install. It can be found in the Control Panel.
Be aware, if you select "Whole Disk," it will reformat the whole disk, and will wipe out any other partitions, including the swap partition. This is not ideal when installing to a hard drive.
I suggest:
Set up partitions the way you want them using GParted, before installation. You can install GParted in Tiny Core, or download Parted Magic, and use it.
Include a swap partition.
If Tiny Core is the only operating system to be installed on the hard drive, set the flag on the partition as "Boot," which is the same as "Active." Do this using GParted.
During installation, you then need to select "Existing Partition."
If you install using this method, Tiny Core should just work.
Be aware:
If you have both Windows and Tiny Core on the hard drive, setting the Tiny Core partition as "Boot," will prevent you from running Windows.
If you are running both Windows and Tiny Core, you may install Tiny Core using this method, leave the Windows partition as "Boot," then install Grub as shown in the links above.