This may be one of the many problems of the Xbox 360 error e68, but you must put in mind that this is very easy to resolve at the same time, you would be able to repair it by yourself with some right guides to help you out.
Once it occurs in your unit, it generally points to your hard disk.
There may be two possibilities, it could be a loose connection with your hard disk cable to the main board or the hard disk overheated in due time.
Of course, we couldn't avoid these kinds of problems, especially if you frequently use your console and not giving it a rest for some hours.
Checking any loose connection between your hard disk and your CPU is one way that you would try and see if the problem is there.
You might want to check any videos or Xbox repair manual if you want to be sure of what you are going to do.
•You can also do a refresh by pulling out your harddisk and putting it back.
•You can opt to remove your storage device and try to see if your game box will function properly without it and not prompting you with a message.
If this occurs, you could already assume that it is a hardware problem and you need to replace it.
•Freeing space in your storage may be an option, but try to assure first that you have a back-up copy of your saved files to avoid any fall backs.
Trying out these few solutions can help you resolve your problem.
You would be able to determine if to buy a new hard disk or you need to repair it by yourself.
If it is under the warranty period, you can opt to have it exchanged with a new unit, but if it doesn't anymore, you need to buy a new hard disk and do the work with a manual guide so that you would save on the cost instead of sending it and spend a fortune on it