I have a Ford F-150 with only 75,000 miles on its 300cid 6-cylinder engine and 5-speed manual transmission. I was surprised when I put it in 1st or 2nd gear and it was as if it was in neutral. The other gears were fine.
Never since it was new in 1989 did this happen, and I've been the owner after my Father died in 2000. It has never been driven in snow and never in an accident. What is up with it?
Your Dad's F-series has either a Mazda or a ZF 5-speed standard gearbox. If you didn't hear any grinding, grunting or loud clunks from the transmission before or during the loss of 1st and 2nd gear, the unit may be salvageable. Especially if there's little or no resistance felt at the shifter when moved back and forth between the two gears.
You may be moving the shifter and little else. It's possible that a retaining pin which holds the 1-2 shift fork to its shaft came loose or sheared off, or part of the linkage even closer to shifter has broken. If it was a major internal breakdown of a gear or synchronizer, you probably would have heard or felt something.
Either way, before ordering a new 5-speed, find an honest and experienced technician who specializes in transmissions. Have him remove the gearbox if necessary and do a partial teardown to determine the fault. No guarantee, but who knows, it may be a $20 part causing you grief. Good luck.