To the best of my knowledge, there are two basic verbal constructions for conveying the conditional meaning. The first one is in the original example of this thread, and Լալով ոչինչ չես փոխի: is an example of the same. However, it is perhaps more informative to make up an example with two verbal clauses, the conjecture and the consequence:
Եթե փող ունենամ, մեքենան կգնեմ։
Եթե փող չունենամ, մեքենան չեմ գնի։
This is what I called the future conditional above. The meaning is basically conjecturing about the future, without any implications on whether it is likely to happen or not. So it is closest to the English first conditional:
If I have money, I will buy a car.
If I don't have money, I won't buy a car.
Note that ունենամ and կգնեմ are different forms, the former playing the role of conjecture, and the latter its consequence. So ունենամ is in the subjunctive and կգնեմ in the conditional mood. Both of them future tense.
The alternative Armenian subjunctive/conditional sentence is indeed in the past tense:
Եթե փող ունենայի, մեքենան կգնեի։
Եթե փող չունենայի, մեքենան չեի գնի։
The main usage is when speaking about a situation in the past that did not happen because the condition was not met.
If I had had money, I would have bought a car. (I didn't have money, thus didn't buy a car)
If I hadn't had money, I wouldn't have bought a car. (I did in fact have money, that's why I did buy a car)
Sorry if I have messed up the English conditionals, I hope the meaning is clear from the explanations.
However this form may be also used for 'wishful thinking' about things in the present or in the future that are impossible or unlikely. Despite it being grammatically past tense. The English equivalent would most likely be:
If I had money, I would buy a car. (implying: it's unlikely to happen now or anytime soon)
In the negative this example doesn't work. But you can say something like
եթե հիվանդ չլինեի, տանը չեի մնա․
If I were not ill, I wouldn't stay at home. (Now or in the future)
This latter usage of the past conditional to speak about the present or the future may be specific to the Eastern Armenian and due to the influence of Russian, where similar construction is used.