No.
A program never ceases to function and the hardware simply goes the way of all flesh, all mineral, all chemical.
If you believe that Machines go to heaven, you'd have to believe that breaking a Microsoft Office 2007 CD would send that whole suite of programs to heaven when really, all you've done is sever a portion of the code making it unreadable. Were it required, the data could be recovered and repaired. Then, would the program be resurrected?
There is something else to a human being - that when it dies cannot be brought back, cannot be fixed, cannot be repaired, despite still-functioning organs.
This implies that while machines are bound to the earth, there is something within the human body which can transcend. The difference between Intelligence and Artificial Intelligence being this something. Whereas the human intelligence or soul has the ability to transcend as it may or may not stem from an ethereal plane of existence, the artificial intelligence was manufactured and stored on Earth, essentially within machine. While the physical location of the intelligence, which in this case is the soul, of the human being is unknown, the physical location of machine intelligence is known, and is unchanging.
On top of that, the absolution of sin was granted to God's children by Christ, not Man's children. Assuming that a Machine could make it to heaven somehow (I don't believe this would be possible as stated above) they coud technically be held accountable for every sin made in their so-called life. I don't think the genocide, the people-growing, the Matrix, et cetera would look too good on their slates.
As far as Eastern religions go:
Buddhism with the concept of Nirvana and the Four Noble Truths could work, I suppose. If a program is broken, a Machine is without power, what does it do? Nothing. There's your Nirvana. More household appliances shoud subscribe to this religion, then, I suppose.
Hinduism could work as well. Samsara is certainly applicable to those programs which are removed from their first hosts, go through the source, and are then put into another host, perhaps performing a different function. Through exile, the desired escape from the cycle could be accomplished as well, where a degree of freedom and englightenment are gained. Karma could be executed through the source - if a program was poor in its duties as a sentinel, it may end up with a recycling function its next time around, as deemed by the great task assigner within the Machine city (Deus Ex Machina?).