Italian inventor Andrea Rossi claims to have discovered cold fusion. There is a history of dis-proven discoveries in this area. How were they debunked and are the arguments applicable to the new case either?
Is the Rossi Focardi LENR true?
They have kept the details secret. I refer to sufficient detail to attempt to reproduce in a scientific research laboratory. From http://www.eetimes.com/electronics-news/4212428/Italian-scientists-claim-cold-fusion-success
It is reported that Focardi and Rossi have had their paper refused by peer-review publications.
Both their effectively refused WIPO patent application and accepted Italian patent lack meaningful detail.
Note the Italian one was submitted just before stricter technical requirements were brought in.
see also http://www.nyteknik.se/nyheter/energi_miljo/energi/article3173090.ece
For example claim 6 of the WIPO patent refers to "catalyzer materials" with no further details.
How were they debunked and are the arguments applicable to the new case either?
They (like any other claim) cannot be definitively scientifically debunked by argument alone, only by multiple independent experimentation trials. Disclosure of full details is a prerequisite for this.
Please beware that there have been numerous professional scams for many years involving claims of cheap or free energy.
If you are more interested in the theory of cold fusion et al then I recommend Physics Stack Exchange