Hi ernest072!
The troubles You've described happening with tc-install reminded me my first TC steps a couple years ago :-)
You make take a look at
http://forum.tinycorelinux.net/index.php/topic,26658.0.html, it is an implementation of "subtractive" approach for TinyCore installation, as opposite to the standard "additive" approach. During "additive" install You start with minimum stuff and expand it with the parts You suggest You'll need. "subtractive" approach captures all necessary and supposes that You will later discard unnecessary stuff.
InstantCore.img is an image of already installed CorePlus14 and TinyCorePure64 in dual boot BIOS/UEFI manner.
Installation process is writing with "dd" of an image to the target drive. The target may be Your HDD, but such shortcut needs extracting Your HDD and writing it on another box. The more convenient and safe way is writing InstantCore.img to USB flash drive, then booting from it on the target computer (in base mode) and self-copying of the USB drive to the target HDD. Of course as You have fully functional TC after booting from flash, You may play around, test compatibility with Your hardware and even download missing stuff - in normal mode. If You are satisfied You reboot into base and dump the USB flash to Your HDD.
Looks like Your computer is functional and have no severe hardware problems, so You may give to InstantCore a chance.
I'm sorry I'm intervening in the standard installation process, just reminded my own unpleasant surprises in the past :-)