Why did you call out engineers?
Did they refuse to come back?
Have you only asked them to attend once?
Well, it depends.
Clearly there is a claim here. They fitted a system which wasn’t at rock bottom price and it doesn’t work properly. There are a whole load of consumer rights issues arising from that.
The question is whether it can be enforced and in what way.
I do think that is the facts are as you say then a court would say that you gave them a reasonable opportunity to repair it. At least you get over that hurdle.
Whether you can claim a full refund is another matter. You are gong to have to show that this system could not work even with repairs to make that remedy one that the court would accept. Courts will always look for the most painless remedy that is available and a repair might well seem attractive.
If that cannot be achieve though then, in theory, you have a claim for the full amount paid.
Can I clarify anything for you?
Not unless they could show that you had brought a frivolous or unreasonable claim. This is a small claims court sum so costs are unlikely.
All the best.
Please remember to rate my answer.