Hi,

This is the clear problem of I/O Hardware. I have the same problem with one of my production server from past few months. You could try to run the DBCC CHECKDB with physical_only option to confirm the scale of damage to your user database.

Only way to come out to the situation is either restore the database from the fresh good backup or run the DBCC CHECKDB with repair_allow_data_loss option. But be sure that by using this command will cost you un-identified data loss, you could not figure out how much and which  data you loose.

If you could manage to find some downtime, you can run the IO stess utility which will report any potential/existing hardware problem to you.

Keep the post updated cause I am also working towards the solution of the same problem and your feedback would add some value to me also.