I am going to take some liberties here with the concept and definition of 'vampire'. Apparently, from what I read, it has been clarified that you are NOT speaking about a 'generic' vampire, but a specific concept that can be modified to suit the requirements. That is, a human body that has been taken over by a virus, which is somehow able to maintain homeostasis and muscular function in the host body without the host body itself being alive (else killing the host body would kill the 'vampire'). I am also assuming that such concepts of 'sentience' and 'memory' in the host are moot points. More a zombie than a vampire - or a cross between them. It is having a moving, semi-functioning body that is important, not any other human characteristics. It, of course, begs the question be asked 'If you cut off the head of a vampire, does it still retain its memory and personality?' I am assuming the answer to this question is moot. The virus somehow becomes the personality, and if there is a brain left in the host, than the virus can somehow manage to keep it functioning in some non-living way enough for the virus to 'read' it. But, of course the destruction of the host memory and personality would not result in the death of the virus.
In which case, the question is not how to kill the vampire host, but how to kill the vampire virus. Since a virus can spread throughout the host, it would imply that any part of the host that remains could potentially contain live virus, which would still be able to reproduce and 'control' the host. That is, it is the virus, and not the host, that actually lives on. This would assume that if any small part of the virus lives, it can propagate again to 'infect' the entire body, or whatever is left of it. A walking hand, where the muscles are systematically triggered by some biological process of the virus? - the virus can either trigger neural impulses in nerves, or it can send out chemical messengers.
So if sunlight and garlic were toxic to the virus, they would result in the death of the virus.
The question then becomes 'How else do you kill this virus?' Certainly, any sterilization process that can be guaranteed to eliminate 100% of the virus, but we know there are viruses that can survive almost every physical environment, albeit in a dormant state. There are viruses that can live dormant in the human body until the body dies, and perhaps even after. Just one virus in one cell of the former host could potentially re-infect.
So why just a stake in the heart? A particular reaction between some protein or other in wood and some cell structure specific to the heart, that produces a toxin that will kill the virus. Perhaps it could even be another virus that lives only in the human heart, that would survive the death of the host, just like the vampire virus. This would assume the circulatory system still functions to some extent to spread the toxin.
This could, perhaps, be molded or refined into some concept of a virus that only lives in the human heart, being the only thing that could produce a toxin under specific circumstances that would kill the 'vampire' virus. It is a solution that does not require the host to be alive in any sense of 'human sentience', or of the heart working as a heart. A dead heart could also host the competing virus.
It does, however, seem to imply some form of sentience for the vampire virus itself.