Ways to write "2000 year old"

According to the Chicago manual of style...

When you hyphenate, it would be with hyphens between 2000 and year and old. So, 2000-year-old, but never 2000 year-old or 2000-year old. Now, to Paraphrase the CMOS for this example...

There is no need for hyphens in “2000 years old.” If you are using a phrase like that to modify another word or phrase, however, you need to bind it together with hyphens (a 2000-year-old grudge). Likewise, use a hyphen if “years old” comes before the noun it modifies (a years-old phobia over wearing the wrong earrings), but leave it open if it follows the noun (the moldy accretion on her cell phone was years old). Finally, you will need hyphens when the phrase is used as a noun (enough pizza for three 2000-year-olds).

So, taking that into account, a 2000-year-old computer would be correct. Or, if you were to rephrase, "a computer that was 2000 years old" would also be correct.

You are right. BBC4 was wrong.

I'd say only the first one is correct.

A book called "English Grammar in Use" is British, and it would put hyphens on both sides of "year."

The last three are definitely unacceptable 'coz once a bunch of words precedes a Noun, they are no longer Nouns but an Adjective. And Adjectives can't become plural in English.

So:

He's 6 yearS old. But... He's a 6-year-old boy.

It's 5 thousand dollarS. But... It's a 5-thousand-dollar bag.

It's 2 hours. But... It's a 2-hour-trip.

Similarly, we say "apple tree" but not "apples tree."

Personally, I believe this is also the reason why they're strung up together like that - to become just one unit describing the Noun (in this case, "computer").