Actually it was a VAX 11/780 system, circa 1978, I was there.
Not on the shuttle itself. Ground based most likely. Here's a link showing the IBM System 4-Pi as the shuttle computer. It's been upgraded, but is still basically the same machine, just a little faster and with more memory. Also called the AP-101 in that application. AP-101S, the upgrade, replaced the core memory with semiconductor memory. (So I was slightly wrong above, but until that upgrade they did have "core")