What did the terminals look like (dirty?)
That sounds like the classic bad terminal problem. It could be a connection
inside the battery tho.
How old is the battery?
Another way to test it is to put it in your car and run it there for a few
days. Keep the "good" battery in the trunk so you don't get stranded somewhere.
Be sure to secure it so it won't be rolling around.

For less than the price of gas to run to the auto store, you can own an
inexpensive little test light that will help you determine if your battery
and/or alternator is goofed up.

They're small, and fit easily in a basic tool box. The test you can run with a
cheapie light is informative, but not complete. A battery can have a "surface
charge" that looks OK, but lack the guts to do any real work.

As somebody else suggested, check those terminals and cable clamps and see if
they got corroded by sitting all winter. The clamp from the jumper cable might
have had enough pressure to make contact through any corrosion, and the austo
parts store would have tested the battery with corrosion-free equipment.