An old car in bad condition

Somewhat old fashioned, and not an adjective like your examples, but a noun, jalopy:

• (Informal) An old, dilapidated motor vehicle, especially an automobile. (AHD)

Comments below suggest adding the following:

Usage example: "We hopped in the jalopy and rattled off to town."

Competitors: Words like junker, heap, and clunker are probably also heard more frequently in the New York than in the south. Jalopy has the advantage of unambiguously denoting an automobile without additional context, which is unlikely to be true of the other words.

Regional note: While it is true that jalopy originated in the USA, it appears to have been adopted in the UK as well, perhaps owing to the American military presence coinciding with the word's peak in popularity. Also note that jalopy has not been surpassed by junker or clunker in either British or American English, according to ngrams, though it must be noted that this does not reflect the spoken language:

English

American English

British English

Archaic: If we take archaic to mean having the characteristics of the language of the past and surviving chiefly in specialized uses (m-w.com) then yes, "jalopy" is archaic, as "somewhat old-fashioned" was intended to indicate. However, a list of archaic words found at http://www.oxforddictionaries.com/us/words/archaic-words-american consists mostly of words that are far less familiar than "jalopy." It appears to be a question of where we draw the line.

It is also possible that jalopy is enjoying a revival, as evidenced by the popular culture references mentioned in the comments.

Banger

noun, British informal

An old car in poor condition: they’ve only got an old banger

More example sentences:

On a family visit to Windsor Safari Park just to get used to his new car, a jumpy old banger with steering wheel stick-shift gears, Ron was flagged down by a policeman.

They are not supposed to be working but their entrepreneurial skills include buying old bangers at the car market and fixing them up for resale.

You can amplify your meaning with the adjective clapped-out:

Clapped-out

adjective, British informal

(of machinery or appliances) worn-out; dilapidated.

Example:

'These same emissions zones will also catch clapped-out old bangers and poorly-maintained lorries and vans.'

You might consider one of the many slang words for such a car -- hooptie, junker, clunker, beater, etc.

Sources: Urban Dictionary and The Free Dictionary.

Here's a noun that can fit your description: rattletrap

From Merriam Webster:

something (such as a car) that is old, noisy, and not in good condition