You need to give us a little more help with this. The "gears are stuck" The first thing that comes to mind is an assumption that you cannot turn the planetary by hand. If that is the case then you have a gear stripped and it has locked up the tower pinion gear or the bevel gear. Both are inexpensive parts and are readily available at any service center or off the internet. With that said you have to determine if you want to fix it your self (you can do it its just time consuming the first time) it will require that you tear down the mixer to it's component parts. you will need to get new gear grease a new gasket and new replacement gears. Then you have to take the mixer apart, remove the old gear grease to get at the worn parts, take the gear housing apart to replace broken parts add new gear grease and gasket and then reassemble, you will more that likely also have to adjust the speed control plate to get the mixer turning at the proper speed again. The gear grease is the kicker, you will have to buy a whole can (30 Oz.) and you will only need 6 Oz to do the re-pack. all parts for the K45SS are available on the internet plus the cost of shipping. You will also need to go to the following site and download your parts list for the mixer, that will give you the proper parts number to order and a schematic to follow along.http://www.kitchenaid.ca/assets/pdfs/literature/Repair%20Part%20List%20-%208212369.pdf
next you will need a clear work area where you can layout the pieces of the mixer so that you can create an assembly pattern that will help you remember the way to put it
back together. you will need a non metal hammer a flat head screwdriver a Phillips head screwdriver a drift punch two rolls of paper towels an empty trash can to dump the greasy paper towels about two hours of time and a calm nature. you will have to open the mixer to determine what parts you need, then you will have to order and wait for the parts to arrive and then do the work. Another option is to take or send your mixer to a service center for repair. if there is no center near you you will have to mail it, and the cost for the service center to repair and send back is going to be $150.00 plus, check to see if you have a small appliance repair shop locally it will probably save you $50.00. If both of those are options that you do not like then it is a DIY repair, that is an easy fix but takes time to get it done. check to see if you have a local shop that will sell you the parts that you need. that will eliminate some waiting time. but the first thing is to take the mixer apart and find out what gears are FUBAR. Now all of this is dependent on weather this is a gear problem or an electric problem that is why i opened with you need to help. What happened when you made the decision that the mixer was froze up? did it make noises? did you hear the motor running but the planetary dint turn? (The planetary is where you put the beaters on). did it smoke? does it make any noise when you turn it on Like the motor humms but nothing turns (That is a gear problem) So as you can see we need some help so we can help you. let us know as soon as you can so we can get you back up and baking.