It’s been hesitating at hwy speed, particularly when taking the foot off the gas while cruising downhill. Then the other day it hesitated at low speeds on the way home. That was the last time it was taken out; today it turned over but wouldn’t start. Fuel pump? Clogged fuel lines? Fouled injectors? It’s not being driven very often.
These are possibilities, especially since it’s not driven often, but there are many more.
How many miles does it have on it?
Has he maintenance been kept up?
When it hesitated, did you get a CEL light?
Have you looked for fault codes?
There’s not enough information in your post to guess at the problem. Has the car been maintained according to the manufacturer’s schedule? Oil changes, fluid changes, spark plugs, timing belt, fuel filter, etc?
118k miles. Maintenance has been faithful to the schedule; oil, etc., chngs have been regular. Ck engine light has not lit at any point.
Faithful maintenance can be very different depending on each individual. I’ll assume oil changes at 5,000 intervals. Other than that we still don’t know much about your car. It is 14 years old with 120K miles. This means all the ignition parts, plugs, wires, cap, rotor, etc. need to have been changed within the last 30K miles. If not, they are suspect. The fuel system could be dirty, or the fuel pump may have died. A dirty fuel filter could also shut you down in the manner you describe.
Get your service records together so a shop doesn’t replace recently installed parts. Pick a shop to do the repair, and call for a tow.