Thank you to all who have weighed in on this question.
Could you get away with using it for the core deposit? Is it possible? Is it ethical?
Drop in used, my opinion.
Meanjoe75fan, I don’t think I understand your answer. Thank you very much to everyone who has responded. I really appreciate it very much.
If the crankshaft rod bearings have gone bad the engine is rebuildable but possibly not cost effective.
If a connecting rod, or plural, was thrown then that generally guarantees the engine is not worth fixing as a thrown rod will often damage the engine block. The cost goes way up.
What meanjoe is referring to about the core is that a reman engine often requires that the old engine be traded in and the engine should be rebuildable. If rod have been thrown and the block damaged then the engine reman company may not accept it as a good core. A core charge may be assessed instead and some reman companies may accept a junk engine anyway.
Think of it as trading in a decent running car and being allowed so much on trade. Now squash the car in a crusher and attempt a trade. That’s essentially what a good core means. 
Thank you ok4450 for clearing that up for me. I understand that now. Much appreciated.The third option, getting the jasper engine for $3500 was based on them taking my current engine. If there is a chance that they may not accept it then may mean another $500.
Can a car with a bad rod bearing like this be driven at all? I just stopped in at my regular mechanic and he said if I can get the car back here he can put in a different used engine with a 5 year warranty. Car is 200 miles away in Michigan. $700 to have it towed back so wondering what you guys think about attempting to go up their and drive it back.
If the engine made a loud clanking sound and then died, it’s toast. Probably a broken piston rod, as others have speculated. In which case, the engine wouldn’t even start. And if it did, it would further self-destruct instantly. Towing is the only option.
Okay thank you that’s what I kind of figured but wanted to be sure.
My mechanic here just told me can put in a used engine that comes with a five year warranty. Or I can have the used engine put in up in Michigan where the car is with a one year warranty. Both around the same price. If still available the used engine in Michigan only had 47,000 on it. Not sure how many miles would be on one from Illinois but I am guessing it may be a lot more based on the year of the car being 2003. Don’t know for sure yet how many miles it would be as he hasn’t searched for one yet. But is a lower mile engine with a one year warranty better or possibly an engine with more miles but with a 5 year warranty? Thoughts??? Found out I can get the car towed cheap with my daughter’s triple A card. Car is three hours away from me at the moment. Thank you all for your opinions. I really appreciate it.
You might be better off towing the car to your local mechanic. A warranty isn’t much use to you when it’s from a shop three hours away from you. Plus, you know and trust your local mechanic.
I’d have it towed to your local guy and have him put the used engine in. Better the devil you know than the one you don’t. 
Thank you jesmed. I do trust my local mechanic, been going there for 10 years, great guys. Part of my confusion is that my daughter has the car in Michigan at college and she is here in Illinois for almost 4 months in the summer and 3 weeks at Christmas. Hard to know which location the car might break down in. Probably 7.5 months total in Michigan vs. 4.5 months in Illinois for the next 4-5 years. But a five year warranty feels more reassuring to me even if I may have to get a trailer hitch installed in case I need to go get the car in the future.
Like I said, I wouldn’t fix it at all. I had my diesel start knocking 150 miles from home when the wife had it. I had a new engine put in at the local Olds dealer for about $2400. It was a rebuilt GM Goodwrench factory engine. Would I do it again? Probably not. Should have dumped it then and saved myself 300,000 miles of problems. You need someone with a pick up truck that can rent a flat bed to go retrieve it rather than a tow company.
Thank you Bing. I am amazed that you had a car that you drove for 300,000 miles. Wow!