Welcome Jim!
As LD1 said, we need more info to give good opinions.
Your machine could be a 580 with no letter designation at all. That's the oldest version of the 580's. (There were also some 530's) If it is truly a straight 580 with no letter designation, you'll to look in seperate manuals for parts for the tractor and the loader/backhoe. At that time the model 33 backhoe and loder were considered attachments for the 580 tractor and not a part of a single TLB unit.
IF you look closer at your engine I think you'll find it to be a 4 Cyl diesel. A 188 diesel to be exact. The 188D is a good solid engine and not too expensive to rebuild in comparison to other diesels.
We need to know about the transmission too. Is it a manual F/R or a powershuttle F/R?
I.E., do you have to push the clutch in to change from F to R?
Unfortunately, the hydraulic powershuttle F/R transmissions weren't all that great.
Hope this helps!
Mark