Q: If I have the Computer (which lets me ignore limits) and someone takes him away or trashes him, do I then have to comply with the current limits?

A: Yup. The same would apply if you have the Batcomputer, or BMO which allow you to exceed the current limits by 1 (or “one” depending on how the card is worded).

The Computer exists both as a regular card in Star Fluxx, and as a promo card available to put in any Fluxx version (though they’re worded ever so slightly differently).