Can't afford a new sink and cabinet any DIY ideas on how to fix this?

Have you tried Habitat for Humanity?

Easy, have it professonally reglazed, will last another 50 years if properly cared for.

Go to Habitat For Humanity Re-Store. Look for a used sink. Your sink is past repairing. Replace it.

Considering that this is probably a builder grade cabinet and sink.... and it looks like the sink is rusted thru....refinishing is not an option and replacement of the sink, at least, will be necessary.... Look around in your area for a store selling construction salvage.. like Habitat for Humanity, etc... see if you can find a recycled/re-purposed unit... You may also find something in your price range on Ebay (local pick-up) or on Craig's list, etc.

We have found some "butcher block" looking counter tops at Lowe's for about $50... just use a really good Marine grade varnish on it...

Pinterest.com or Youtube.com should have a tutorial on how to cut the new top to fit the new sink.. (if you were not able to find a sink and cabinet unit at the salvage store)

is the porcelain intact? if not, you will have to get it re-coated. some stores may have a kit for that, but it may have to be someone that does it as a business. If the porcelain is good, try to use CLR = a product for rust .

That looks past repair with an epoxy repair kit, so I think I would look for a used replacment at Habitat for Humanity, and architectural recycler, or convert a stainless steel bowl to a sink to replace it.

https://www.youtube.com/watch?v=GKgi8YiAQx8