"Stuttering" start

When starting, especially in colder temperatures, the engine start is interrupted by a “thud” sound. The start occurs after this one-second “interruption” while I keep the key in the start position. This interruption occurs only once, usually when first starting in the morning. Subsequent starts are normal,
unless the car has not been in use for a few hours. Then the “first start” problem re-occurs. The starter motor has been replaced. No improvement.
When the problem first began a few monts ago, very intermittently, the gauges in the dashboard would not register as would normally happen and I could
hear a whirring sound for a few seconds. Then the gauges would perform as normal. This is a 2004 Taurus with mileage of 64,000.

Check your main power cables. Look underneath the insulation for corrosion. Clean and tighten all of the connections for those - not just the battery terminals. Have your battery load tested.

The whirring sound may be the fuel pump. That’s probably normal.

Ask your mechanic to measure the voltages at both terminals to the starter motor during attempted cranking. Measure beween the terminal and the starter case, with everything connected. If either is below 10.5 v (during cranking), the cause needs to be investigated.