2000 Olds Intrigue won't start

I have a 2000 olds, Intrigue 102,000 miles and daily when I turn the key it will not turn over at all. Here's what happens. Sometimes I get in turn the key and it starts right up. Sometimes I get in and there is nothing it won't turn over, if I turn the key to start it a few times then turn it and hold it all the way over, I'll hear a sound like a relay opening and in about 10 to 15 seconds the car starts right up, this always works but its a pain if your in a hurry. It doesn't happen every time but usally several times a day, and there is no time span in between when it won't start, some times its a few minutes sometimes 8 to 12 hours. I did have a new computer installed in November and thought that fixed the problem but it came back in a day or so. Anyone out there have any ideas?
Thanks
Paul