Please could someone advise on the following issue:

Route: MAN-LHR-JFK-LIM
Ticketing carrier: AA (all AA flight numbers)
Operating carriers: MAN-LHR (BA), LHR-JFK (AA), JFK (LA)

When checking-in at MAN, BA only gave me boarding cards for the first 2 sectors, but said I would need to go to the transfer desk at JFK to get boarding card printed out. I double-checked at Heathrow with AA and was told the same thing. The connecting time at JFK was pretty tight (1:15), but the flight from LHR as 15 minutes early, giving me 1:30. I got through immigration and customs really quickly and got to the One World transfer desk about 45 minutes before scheduled departure. It was at that point LAN informed me I was not checked-in for the JFK-LIM flight and the flight had been closed and therefore I would not be accepted for boarding.

AA rebooked me the next morning via MIA resulting in a 10-hour wait in the airport (and they refused to provide accommodation or food) and arriving 15 hours late to my final destination.

- Why did BA not check me through to my final destination (it was no issue checking my bags to LIM)? Is it true that sometimes an airline can't check you all the way through? If so, how can a 1:15 MCT even be permitted?

- Which of the 3 airlines is responsible for this sequence of events? BA say it's AA's fault, AA say it's BA's fault, LA say it's not their fault...

- Is there any scope for requesting/demanding compensation? Is there any legislation regarding this? It wasn't a cancellation and LAN may say I wasn't checked in, so therefore it's not denied boarding. So what it is? Negligence on the part of the check-in staff? Inevitable eventuality when travelling on codeshare flights?

Any help would be greatly appreciated.