Did Thráin have one of the seven rings?

Question

In the Hobbit film it emphasises Thráin's lust for gold and the insanity this bought on.

Was this caused by only the gold, or did he posses one of the Seven rings given to Dwarfs which could corrupt?

Answer 1

In the books yes, the Lord of the Rings tells us this.

‘Balin will find no ring in Moria,’ said Gandalf. ‘Thrór gave it to Thráin his son, but not Thráin to Thorin. It was taken with torment from Thráin in the dungeons of Dol Guldur. I came too late.’ ‘Ah, alas!’

^{The Lord of the Rings | THE COUNCIL OF ELROND}

The film messes the timelines up a bit, in the books Thrór is King under the Mountain when the dragon attacks and goes a little crazed with long wandering, giving the ring to Thráin before attempting to take back Moria single handedly.

‘Surely you do not think of returning to Erebor?’ said Thráin. ‘Not at my age,’ said Thrór. ‘Our vengeance on Smaug I bequeath to you and your sons. But I am tired of poverty and the scorn of Men. I go to see what I can find.’ He did not say where. He was a little crazed perhaps with age and misfortune and long brooding on the splendour of Moria in his forefathers’ days; or the Ring, it may be, was turning to evil now that its master was awake, driving him to folly and destruction. From Dunland, where he was then dwelling, he went north with Nár, and they crossed the Redhorn Pass and came down into Azanulbizar.

^{The Lord of the Rings | Appendixes - III DURIN’S FOLK}

The characters and traits of Thrór and Thráin have been somewhat merged in the films.

Answer 2

Yes.

Thrain's Ring even has its own page at the LotR Wikia.

In canon:

Of this Ring something may be said here. It was believed by the Dwarves of Durin’s Folk to be the first of the Seven that was forged; and they say that it was given to the King of Khazad-dûm, Durin III, by the Elven-smiths themselves and not by Sauron, though doubtless his evil power was on it, since he had aided in the forging of all the Seven. But the possessors of the Ring did not display it or speak of it, and they seldom surrendered it until near death, so that others did not know for certain where it was bestowed. Some thought that it had remained in Khazad-dûm, in the secret tombs of the kings, if they had not been discovered and plundered; but among the kindred of Durin’s Heir it was believed (wrongly) that Thrór had worn it when he rashly returned there. What then had become of it they did not know. It was not found on the body of Azog.

None the less it may well be, as the Dwarves now believe, that Sauron by his arts had discovered who had this Ring, the last to remain free, and that the singular misfortunes of the heirs of Durin were largely due to his malice. For the Dwarves had proved untameable by this means. The only power over them that the Rings wielded was to inflame their hearts with a greed of gold and precious things, so that if they lacked them all other good things seemed profitless, and they were filled with wrath and desire for vengeance on all who deprived them. But they were made from their beginning of a kind to resist most steadfastly any domination. Though they could be slain or broken, they could not be reduced to shadows enslaved to another will; and for the same reason their lives were not affected by any Ring, to live either longer or shorter because of it. All the more did Sauron hate the possessors and desire to dispossess them.

It was therefore perhaps partly by the malice of the Ring that Thráin after some years became restless and discontented. The lust for gold was ever in his mind. At last, when he could endure it no longer, he turned his thoughts to Erebor, and resolved to go back there. He said nothing to Thorin of what was in his heart; but with Balin and Dwalin and a few others, he arose and said farewell and departed.

Little is known of what happened to him afterwards. It would now seem that as soon as he was abroad with few companions he was hunted by the emissaries of Sauron. Wolves pursued him, Orcs waylaid him, evil birds shadowed his path, and the more he strove to go north the more misfortunes opposed him. There came a dark night when he and his companions were wandering in the land beyond Anduin, and they were driven by a black rain to take shelter under the eaves of Mirkwood. In the morning he was gone from the camp, and his companions called him in vain. They searched for him many days, until at last giving up hope they departed and came at length back to Thorin. Only long after was it learned that Thráin had been taken alive and brought to the pits of Dol Guldur. There he was tormented and the Ring taken from him, and there at last he died.
_{-- Lord of the Rings, Appendix A, Part III: Durin's Folk}