My first attempt to boot Tiny Core 9.0 failed. I messed around for a while, asked Mr Google for help, and after maybe 15 minutes came up with something that ran. The short answer was to add the kernel boot parameters:
nomodeset acpi=off
I found the comment:
However, many hardware platforms ship with buggy or out-of-specification ACPI firmware which can cause any number of unspecified problems. If the machine is randomly powering off or failing to boot, disabling ACPI may help.
Unfortunately the only download I could find associated with the ViewSonic SC-T45 was 'ViewSonic Device Manager Software_2.08.036'. There was no sign of an updated BIOS.