Who do I contact for a dead Echo Show

Summary:
approach trader as trader holds the statutory and legally enforceable product durability obligations for up to 6 years.
Manufacturer / brand owner may offer a warranty but such warranty is non-enforceable, and for subject product is believed to have expired.
But:
manufacturer / brand owner may offer post-warranty incentive as gesture of goodwill to retain potential future business with consumer - maybe a discount on replacement, assuming the consumer would wish to expose themselves to purchasing another low-durability product.

Detail:
Any product's statutory quality and durability obligations rest with the trader that sold the product - for up to 6 years since receipt (unless you live in a country that shafts its citizens by enforcing lesser period of 5 years, such as Scotland).
If you believe the product should have sufficient durability to perform flawlessly since

a year or so back

and you haven't exposed the product to unreasonable abuse such as permitting it to be chased around your garden by your aggressive pet goldfish:
you present the prematurely busted rubbish to the trader that sold it and inform the trader that you wish to have the bustedness resolved by the trader under Consumer Rights Act.

If the trader attempts to divert you to the manufacturer when you ask the trader the question:

is (name of trader) exempt from Consumer Rights Act ?

the trader will either:
• play ball and inform you how it will process your CRA claim (that may or may not involve you obtaining independent functionality opinion)
or
• expose itself to all manner of legal dullness by telling you some rubbish that CRA doesn't apply, even though it does. Make a note of any such hilarious suggested exemption in front of the trader's staff & repeat it to them to clarify your note is accurate, then post the (non)exemption excuse here

Additionally:
no idea of the spec being pedaled by Argos

a year or so back

but current marketing dullness stated by Argos for Amazon Echo Show 5 3rd Gen Smart Speaker is

Manufacturer's 1 year guarantee.

Maybe it has the deep reset like Amazon Fire tablets? Google reset and factory reset for Echo Show. That's how I fixed a failing to charge beyond to 50% issue on an Amazon Fire tablet. It could also be a faulty power supply, try borrowing someone else's Echo Show power supply to check.