1996 Chevy Suburban starting prob

1996 Chevy Suburban V8 Two Wheel Drive Automatic 205k miles

Whenever it rains or theres alot of moisture in the air, my suburban wont start. It cranks until the battery runs down, then when I put a jump on, I have to crank more, finally it starts to catch and then finally, she turns over. After that, she is fine untill the next bout of rain. Help!