Here are some basic specs on your 580. Not as complete as an Op. manual, but it will give you fluid capacities on you oil, and coolant. Also look up towards the top where it says "more JI Case 580CK specs", and click on it. It will give you the loader height, etc.
TractorData.com J.I. Case 580 CK Construction King industrial tractor engine information
For parts, go here:
CASE
Place you cursor on "parts & service". A drop down menu will appear. Click on " Search for parts".
On the next page, click on "Launch parts catalog" in yellow.
A top left, in the white block where it says "model" type in "580", then click on "search". All 580 models will appear in the next menu. Scroll down 7 lines, to "580 Construction King Tractor", and click on it.
Below will appear "Figure listing" Click on that. On the next page that appears, every component, or section of your tractor is listed. Click on a selected section, and on the next page, an exploded view of that section, or component will appear at the top right. Below, will be part numbers, and description of said part.
If you are familiar with "copy and paste", you can copy a part number, and paste it on a search engine, such as Google, to shop for parts. I've always gotten more hits on Google, when searching for something. It kinda' helps a lot with sticker shock too... Usually Coleman Equipment, a Case dealer will be on the first page of hits. They post Case Dealer prices. A good way to compare, if you don't mind using aftermarket parts.
For the backhoe, and loader attachments, they are at the top of the listing, above the tractor parts.
Service/Shop Manuals can be found on Ebay. Expect to pay $150.00+, for an OEM Manual. Sometimes you find one for less, you'll just have to shop some.
OEM Manuals are tough to beat. Expensive yes, but well worth the money. I got one for my 480C on Ebay, and it's like "Case Backhoe's for Dummies" They take you through step by step on procedures, from removal, to reassembly. Lots of pictures too... Mine is approx. 4" thick, so LOTS of info.
OEM Op. manuals can be found on Ebay too. I'd guess $20.00+ for those. Handy for capacities, hoe & loader lift & reach specs, machine weight etc.
If by chance, you need brakes on your unit, the link below had the best prices I could find on the net. They have many other parts also, if you happen to need anything.
Remanufactured Transmissions, Torque Converters, Engines - Joseph Industries
By copying, and pasting the part numbers, you can shop online for the best deal. Joseh Ind. beats others hands down, and seem to be decent parts, although from across the pond.
I previously had a 310B, and now the 480C, and they pretty well used the same components, such as the main trans, brakes etc. If you get into something on yours, you're not sure about, be sure and post. I did a lot of work on the 310B to get it in shape to work, and some on the 480. I'll help with what I can...
Hope this helps...