It is possible that you are talking about Japanese ryokan (Japanese inn) at Hakone called
Taiseikan (対星館). There is a personal
website (website is in Japanese but there are pictures) showing the cable care which used to be at Taiseikan.
Due to age of this cable car, on May 2009 the inn replaced this cable car with small monorail looking people mover.
Unfortunate news for you is that Taiseikan has closed on August 2013. which is not mentioned on their English website. Japanese website of Taiseikan has short comment indicating Taiseikan will re-open after the renovation. In Japanese internet sites there have been few inquiry as to update of the renovation of Taiseikan, if there is specific date of renewal opening. However, there seems to be no update of Taiseikan. It has been six years since Taiseikan has closed and some are wondering it Taiseikan will ever reopen.