You mustn't warn people against buying from Comet on the basis of a single bad experience.
Under the terms of the recently revised sale of goods to consumers regulations the law assumes that the fault existed at the time of purchase. You don't have to prove anything. The retailer (NOT the manufacturer) is liable for the fault, and must either replace the product, refund your money, or carry out the necessary repair.
This is where we hit the stony ground.
Most retailers have not got the means to repair a computer, and they will invariably send it back to the manufacturer - the law allows them a 'reasonable' time to do this, but doesn't define what reasonable is in this context.
Non of which need have bothered you, because your computer was not 'fit' for its purpose under the terms of the Sale of Goods act, and you would have been able to reject the machine and ask for a full refund or a replacement. As it's turned out, you seem to have a fully functional computer - albeit after a week's delay.