I tried to adjust my valves, following the directions in the manual
word for word. I was very careful and took my time. When I was done,
it started up and ran just fine. I proudly watched a smooth-running
engine for about 2-3 minutes before turning it off. But when I tried
to restart it later, it would not start. The starter just keeps
turning it over without results. The sparkplugs are like new and
correctly gapped. The distributor cap and rotor are same. What's
going on?

Are you getting a spark to the plugs? You can check this by taking a wire out from a spark plug and attaching a known good spark plug to the removed wire. Hold the threaded part to any unpainted metal part of the engine. When holding the spark plug, wear rubber gloves or wrap it with some paper towels, otherwise you will get zapped. Have someone else start the car for a quick second. Reply with your results.

Figured out it was a bad coil...thanks for your help!