replace axel's in order to test failed transmission

Ok to start with the likely hood that your car busted one axel is not likely but two is almost impossible so i would checkout another shop and it sounds more like the clutch packs in the transmission went out so i would try having that rebuilt before i spend money on the axels

It is easy enough to determine if the axle is the cause of your problem. start the engine and put it in gear if one of the axles turn and the wheels don't then replace that axle. If the transmission behaves correctly then replace the other axle if it is worn or has broken boots. The trans maybe damaged internally, the F clutch can fail causing it not to drive. C clutches commonly break the aluminum housing at the clip ring groove on the Heavy Duty ZF trannys but you only loose reverse gear.