There is likely a "do not use after" date molded into the plastic somewhere, but it may be quite hard to find. Plus, as Wendy pointed out, that seat was discontinued so long ago there is no chance that it's still within its "useful life."
There are many reasons why car seats expire, and even if it's in perfect condition it still does not compare to what is currently available. I believe that seat has a 22 lb weight limit for rear-facing, for example. It is now recommended that children remain rear-facing as long as possible, and most currently available car seats had rear facing limits of 35 or 40 lbs. We encourage parents to choose car seats that will fit their children rear-facing until a minimum of age two, which for an average-sized child is pretty much any car seat you can find (even the $38 Walmart one).
If you can give us an idea of what your budget might be, the size of your child, and what vehicle you'll be using it for, we can make some suggestions for you.
As for the Century car seat, many communities have car seat recycling programs available. If you have trouble finding one near you, we may be able to help with that as well.