I think you found your only, or one of possibly two culprits. A crack in the air inlet hose will result in a huge vacuum leak. Since your car relies on vacuum, a huge leak will result in your car starting, and then almost immediately stalling. Further, often times, washing the car, or rainy days, will result in a no-start or poor running condition if your distributor cap has a hairline crack in it. If your cap and rotor are original, they are just as suspect as the air inlet hose. I wouldn't worry about rodents unless you see bits of acorns...

Hope this helps,

Chris