Does "drag" mean turn over slower than expected? Is the car starting? When you hear the click it means current is getting to the starter solenoid, but if the engine is not turning over, not enough current is available to crank the engine. Generally that's a sign of a weak battery. Since the battery has been checked, there must be a drain somewhere. I'd check the battery cables, Clean the battery terminals and connectors. Check the condition of the cables themselves. A degraded/cracked cable could be draining off just enough juice.
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