Car stalls on the highway?

Recently purchased the LX version of the Honda Civic with 500o miles. I drove it from California to Canada and it is very cold this week. The car stalls on the highway (just cuts out) and is hard starting. It wont start at all if left a lengthy period of time. I am told the rad has almost nothing but water in it. As well the only car key I have looks like it is cracked and wobbly and the computer chip inside may have been compromised. Would either of these things be the cause of the problems? The car will crank and often it takes about 10 secs of cranking to get it going after a stall.