HP Repair Reached 20-Day Mark, No Replacement No Real Help

I requested a replacement for my computer as it reached the 20-day mark, but they refused, stating that the usage period hasn't exceeded six months. Instead, they instructed me to send my computer to the company I bought it from for replacement. To expedite the process, I waited for the part to arrive before sending it. However, when the part arrived on Monday, the service informed me that it was incompatible, and they had to order a new one from abroad. My computer has been in service for a month now, and they provide no assistance other than updating me on the process. Why isn't the immediate replacement of a 3-4 month-old device with a new one happening when the part is incompatible? Why is there a shortage of parts, and why is nobody providing information? The system indicates the part will arrive on December 1, but the authorized person claims they can't see the date. If my computer doesn't arrive by next week, I will initiate legal action, or I demand that someone authorized address this matter promptly.