Q: The clutch was slipping, started working fine again, and shortly thereafter it wouldn't shift out of neutral.

If the clutch is slipping while "released" (engaged with the flywheel), the clutch friction material must be replaced as well as possibly other components such as the pressure plate, throw out bearing and other components. In addition, the flywheel has to be inspected (measured for runout) to see if it is serviceable. Glazed or damaged flywheels can be re-surfaced to some extent but it is possible you might need a new flywheel. There is some concern of course if there is coincident damage to the transmission. Prior to repairing the clutch, the condition of the transmission should be ascertained so that "all" problems are solved at one time. It would be ashame to install a new clutch only to find out "later", when everything is back together, that you have internal transmission problems as well. To determine what all is needed, I recommend you request a clutch system inspection. At the conclusion of that, the mechanic will give you your repair options and costs. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.