I put a cassette into the tape deck; an iPod accessible tape. It was rejected but the tape deck spindles keep spinning even with the car off.

Replace it with an after market stereo. It is an internal problem. Not worth fixing, even if you know about electronics.

unless there is a specific jack to connect it you cant unless it has a tape deck then you can use a wired cassette adapter for it..most newer radios are set where you can use the celphone hands free and you can program the phone to send its internal music through the bluetooth hookup.

sounds to me like your tape belt in the other motor has broke ,the drive for the tape deck has a rubber band putting it crudely and these belts are a special rubber ,it should be a easy repair but make sure you get the right size rubber band but they must be made for a tape deck and not one from office draw

The radio checks to make sure the drive capstan is turning - if not, gives the E10 error. Either the drive belt in the radio is slipping or the drive wheel in the adapter is sticking. If it does it with a real cassette, then it's probably the drive belt. If not, you can try to figure out why the wheel in the adapter is not turning freely.

Cassette decks have sensors on the reels which tells the deck when the tape is at the end. When the reel stops the deck switches the direction of the tape and sometimes the position of the head(depending on the deck design). Most common problem is the tape is hard to turn, or the deck won't turn it ( deck thinks it's at the end, click, still won't turn, click, won't turn, click) you should fast forward and/or rewind your tapes from start to finish once in a while to keep them lined up(narrow spool/less friction), you shouldn't have to but it works. BUT,...your problem sounds like a slipping or broken belt/or dirt causing the problem. Take the deck out to have a look and clean the capstans(rubber rollers)belts,heads with alcohol and a Q-tip while your at it. Dirt's usually the main culprit and if you do have some other problem, cleaning it is always a win/win (It will also sound better clean)

The switch inside the tape player needs to be cleaned or replaced. The dealers send out all radois to a repair shop that is an authorized repair facility to perform this type of work. Shop mechanics do not repair radios or tape decks at any dealer I know of. It may be far less to replace your ciurrent unit with an aftermarket one unless you want to keep your factory unit instead. Many top shelf radios are out there and most can be found at stores like Best Buy and even Car Max these days

buy a different tape adapter the one you have is too loose or you deck needs both wheels to turn 1 driving the other if this doessnt happen it will keep changing sides

No, there isn't. The only way I know to remove a cassette when the 'Eject' function doesn't operate, is to remove the audio unit & disassemble it to the point you can access & manually turn the gear(s) of the 'eject' mechanism. In the process, you could possibly discover where/what the problem is and fix it.

Since no repair parts or repair manuals are made available to the consumer by GM then you must remove the deck from the dash and send it in for repair at a factory approved repair center.

clean it this can do alot dont know if yopu have done this but trty it some times its the simple things that work