17 people have read this and do not appear to have the answer (or are being selfish in not sharing it)

That would all depend on if the priest was indeed validly ordained by the old rite, and if he absolves you.  The priest must absolve you, he can retain your sins and if this "priest" is a pretender or infiltrator, to begin with, doesn't even believe in absolving your sins, he just sits there and enjoys listening to your guilt.

However, if the person is sincere in the wanting to make a good confession, and is truly sorry for their sins, doesn't know the difference between a pretender priest, or a priest in good standing with God. In other words just ignorant of the fact that the novus ordo is not Catholic but a new religion absent from the power to forgive sins.  I believe God will forgive the penitent for He and He alone will know the situation and state of mind of the penitent.  

When in the future this same person realizes the truth of what is happening and is now convinced that he/she was led into a false religion but now has found their place through a Traditional group, they should make a general confession.    

That would all depend on if the priest was indeed validly ordained by the old rite, and if he absolves you.  The priest must absolve you, he can retain your sins and if this "priest" is a pretender or infiltrator, to begin with, doesn't even believe in absolving your sins, he just sits there and enjoys listening to your guilt.

However, if the person is sincere in the wanting to make a good confession, and is truly sorry for their sins, doesn't know the difference between a pretender priest, or a priest in good standing with God. In other words just ignorant of the fact that the novus ordo is not Catholic but a new religion absent from the power to forgive sins.  I believe God will forgive the penitent for He and He alone will know the situation and state of mind of the penitent.  

When in the future this same person realizes the truth of what is happening and is now convinced that he/she was led into a false religion but now has found their place through a Traditional group, they should make a general confession.    

This Post is by JPaul

I'm sure I will be corrected if I'm wrong. 
With the New Rites of Ordination to the Priesthood and "Installation" of a Bishop, it appears things have changed a bit.
The "Instalation" (not Consecration) of a Bishop following the 1968 changes, does not give the Bishop the right of Consecration, but strangely adds the right to forgive sins. (which is in the pre-Vll priestly ordination)
In the new NO ordination of the priesthood, along with the elimination of the minor orders,(exorcist, porter and I forget what else) It OMITS the ability to forgive sins. I was trying to docuмent this but I cannot and if anyone has the docuмentation, I would appreciate it.
Apparently the validity of the Bishop is determined if the Bishop was consecrated BY a Bishop prior to the new rites of 1968 who had the right to consecrate. Then he would be a valid Bishop. Today a valid Bishop could ordain priests in the Old Rite and they would be valid priests, even under the NO banner. For example, if a Bishop, who was consecrated validly by a Bishop consecrated in the old rite, ordained priests in the Fssp or ICK, they would be valid priests capable of valid confessions.
I suspect that the possiblility of having valid Consiliar Traditional priests is getting smaller and smaller as real Bishops pass away. 
I

NO!  Priests of the New Order do not have valid ordination.  When the Precious Blood is not available in the sacraments, we get no sacrament.  We have a perfect contrition until we have a valid Priest.  Holy Mother Church understands/recognizes Perfect contrition.  Holy Mother Church understands there will be times like this, it is in prophecy that the continual Sacrifice of the Mass will end.  If and when it finally does, confession and other sacraments will end?  We do our best and our best is not New Order, or any who come under dioceses.

Achbishop Lefebvre, who is a much more trustworthy source than you, says otherwise.  

You are correct.  I do not know which rite is used for FSSP and ICK priests.  I suspect the new rite.  In any event, they are certainly not in a position to insist on a validly consecrated bishop--Frank's head would spin and they'd be disbanded faster than you could say neo-pelagian.

FSSP priests are ordained in the traditional rite by bishops who, almost universally if not universally, were consecrated in the new rite.  Thus, it really doesn't matter whether what rite is used to ordain them.  The bishops ordaining priests were consecrated in a rite that is invalid so their actions have no affect.  Such priests are no more Catholic priests than your local Lutheran minister down the road.