Starter problem for 2005 Honda Accord

Court cases can be a toss-up. The most you would be entitled to is a refund of everything you paid them or that it has cost you to make it right.

If you can get a current shop to sort it out and write you up a brief tech explanation of the problem and the cure you could always send a registered letter to the first shop asking for reimbursement. If they refuse the next step is small claims.

It’s possible they could pony up rather than go into court. The final disposition would depend upon the attitude of the judge. If you do go into small claims court I will add this.
Keep your complaint as simple, short, and low key as possible while showing respect to the court.
Small claims judges do not want to hear a long story about what happened nor do they want to hear any back and forth between the plaintiff and defendant.
Address all answers and comments to the judge only.