If some villian melted kryptonite into a liquid form, and the liquid was then injected into Superman's blood stream, would it permanently limit his powers? Would it eventually kill Superman?
Superman's cells absorb electromagnetic radiation from yellow stars (like Earth's sun) which powers his super powers. Kryptonite's radioactivity interferes with this semi-photosynthetic process, driving the energy out of his cells in a painful fashion.
So, as long as this radioactivity interference exists, his super powers would be blocked and he would be dead in the end.
As there's no sufficient canonical documentation of Kryptonite's attributes, it can't be said that it can be melted or not. Also, its not necessary that it'd possess radioactivity in non-crystalline form.
This raises the interesting question of whether or not Kryponite could be liquified. But to answer this question if somehow Kryptonite was liquified and injected into Superman than he would most likely die. The danger of Krypotonite to Superman is the radiation that comes off of it. So as long as the radiation isn't changed when turned from a solid state into a liquid or even a gas then it would still hurt and could always potentially kill Superman if he receives a long enough or direct enough exposure. I'm pretty sure that a dose of lethal radiation normally kills or permanently harms anyone exposed to it so a radiation that harms Superman would have the same effect on him.
In Batman v. Superman, Kryptonite is introduced into Superman bloodstream via his respiratory system as a gas.
The pathology is as follows:
For the first 30 seconds, while breathing the gas, he coughs, gags, seizes up, and spasms, unable to make himself move, and clearly in pain. However, he remains conscious and can still hear Batman's taunts.
Even before the gas cloud completely disperses, Superman is back on his feet and- apparently- unaware of any compromise to his powers or facilities. He strikes out at Batman and is surprised when Batman blocks his punch. This differs from his experience of Kryptonite Atmosphere where he expressly says that he feels weak and collapses unconscious... yet otherwise, suffers no further harm from the gas. Here, it is apparent that continual exposure to Kryptonite could kill... yet how do we account for his continual powers and recovery?
Unlike Kryptonite Atmosphere, Superman clearly still retains a modicum of his powers. Batman stomps on him wearing a 250 lbs suit with spiked-soled boots from 1.5 stories up. He kicks him across the floor. He punches him with metal gauntlets without bruising. Superman still has durability and throws Batman through a wall and across a room, so he still has strength. 90 seconds after the first phase of exposure, his invulnerability returns as does his power of flight.
What's happening inside?
It's clear that his power-granting organs are under attack, but that his powers are still in effect and in a sense fighting back.
It seems that Kryptonite has a relatively short biological half-life with Kryptonians. Typically for radiological materials, the biological half-life can only be shorted by elimination and expulsion from the body. However, it's clear that Kryptonians have a special relationship with radiation. That makes it possible they have organs meant to manage, filter, and contain bad radiation the way our bodies have livers to break down alcohol or kidneys to clear our blood of toxins. In the same way ingesting Potassium Iodide can protect your thyroid gland from radiation, Kryptonians may have a similar bodily process for surviving bad radiation.
Therefore, based on dosage, either the Kryptonite overwhelms these processes and powers (like regeneration)... or he makes a gradual recovery.
Addendum, towards the end of the New 52, Superman was actually able to metabolize the radiation from Kryptonite as a source of power, albeit to terminal effect. It's suggested, however, had his issues not been compounded with two additional traumas, he might have recovered.
It depends also on if the "needle" could be able to penetrate Supermans skin to be able to seep the kryptonite into his blood because the needle might just snap in half or something and not even go through his skin.