Not going into gear 1996 Buick Park Avenue Ultra

I have a 1996 Buick Park Avenue Ultra. It has a four-speed automatic transaxel and a 3800 Supercharged L67 engine. The car has just over 152,000miles on the odometer. I have recently have been having problems getting the car into gear. I sometimes have to pull the gearshifter up and down for 20 minutes to get it to move. The gear shift will show that I am in drive or reverse, but the transmission stays in park. Once it "clunks" into gear, it runs fine until it is put back into park. Is this a problem in the linkage or is this a transmission problem? Thanks for the help That's almost definately a transmission problem. The 4T60E's are known for having problems. Look under the hood and find the shift cable. Have a buddy or wife or anyone with legs and arms move the shift lever for you. If the cable moves freely, then your problem is inside the tranny, either with the valve body or the control module or solenoids that control the shifts. Also, is there a check engine light on? If there is pull the codes. Get back to us soon. Also, duh i forgot the most obvious. Check your fluid level. If it's low fill it obviously. If it's full but ot a pink-bright red color, take it in and have it changed. I've seen a simple flush and fill work wonders. Just thought I'd let you know a couple months back my car was doing the same thing - - in my case it was most definitly the transmission! Within 3 weeks it went from doing that occasionally to only having first gear when it went into drive - which made a normally 2 hour drive home along county highways VERY interesting. All in all-try not to delay on this repair!!!!!