Richard, I'm reading Lawrence a little differently.
Lawrence, is it the case as suggested by Richard, that when you turn the key to the 'on' position only, that the starter motor engages to crank the motor, or is it that when you turn the key to the 'start' position, the starter engages but struggles to crank the engine?
If it's the latter, then connect a voltmeter across the battery terminals - should read around 13 volts, then with the meter still connected, turn the key to 'start' - voltage should only drop to around 8 volts. If it drops significantly more than this, then suspect a bad battery.
Best to have someone else turn the key while you hold the meter leads directly on the lead posts of the battery.
If volts are ok, then it must be a bad connection, either battery terminals, neg at engine or pos at starter motor, though these types of problems 'usually' make the starter solenoid rapidly click in and out as well.
From your description, my money is also on the battery. Good batteries have been known to suddenly go high resistance in one cell, for no apparent reason.