Stars convert mass into energy. Even converting the slightest mass into energy is immense because the speed of light is so great and $E = mc^2$. This means that stars have to emit large amounts of energy. So can they emit so much energy in a form of electromagnetic radiation that is not visible light? Resulting in a star that cannot be detected using our senses(+ a telescope). If so what problems could this star pose?
Light that is not light
That's meaningless. All light is electromagnetic radiation. A finite part of the infinitely large range of the electromagnetic spectrum is visible light. So you should talk about EM radiation and to discuss the visible spectrum just say visible spectrum.
Stars emit lots of energy at frequencies that are outside the visible range.
Dark matter does not mean that it's just not radiating in the visible part of the spectrum. It means it's not radiating in any part of the EM spectrum much. If dark matter exists (and that's not certain) it won't interact with most matter much at all.
If dark matter were in star-like objects, it sounds very unlikely that there would not be any EM radiation as a result of the interactions that would result in a star-like object. We'd detect it if it were there. So I don't think that's likely.
You mix up a lot of things in your assumptions.
Stars convert mass into energy.
$E = mc^2$
The way stars produce energy is nuclear fusion. One main process there is the tripple-alpha process, which releases a net energy of about $E \sim 7$ MeV (that is not that much)
So can they emit so much energy in a form of light that is not light?
By light you are speaking of visible light. But radiation goes over all frequencies and wavelength, not just the one the human eye can see (which is roughly $\lambda = 400 - 700$ nm). Here you want to check out the theory behind black body radiation, which describes - more or less - the intensity of the light at different wavelengths/frequencies at a given temperature.
So can they emit so much energy in a form of light that is not light? Resulting in a star that cannot be detected using our senses(+ a telescope).
Presumably by "light that is not light" you mean light outside of the visible spectrum. This is why the fields of gamma ray astronomy, x-ray astronomy, ultraviolet astronomy, infrared astronomy, microwave astronomy, and radio astronomy exist. Astronomy is not limited to the visible spectrum, and there's lots of interesting stuff to "see" from using a telescope that senses light outside of the visible spectrum.
The hottest of stars emit most of their radiation as x-rays and ultraviolet light, but they also emit a lot of visible light. These very hot stars are quite large, short-lived, and very rare. The coolest of stars emit most of their radiation in the infrared, but they also emit some light in the visible range. These very cool stars are quite small, very long-lived, and extremely numerous. Their cool temperatures makes them rather hard to see, even in the infrared.
If so what problems could this star pose? Could this be dark matter?
The very smallest of those cool stars, along with black holes, cool neutron stars, brown dwarfs, and rogue planets collectively form a set of candidates for dark matter called "massive astrophysical compact halo objects", or MACHOs for short. However, theoretical calculations along with observations says that MACHOs can account for at most about 20% of dark matter.
I will just point out two things that haven't really been discussed above.
Firstly, stars generally fall into two categories. 'Hot stars' are those that convert mass into energy by nuclear fusion, and 'cold stars' are those that have ended the nuclear burning phase, e.g. white dwarfs and neutron stars. These still have a finite temperature and therefore will emit radiation. As you can imagine, however, since they no longer produce energy, eventually they will become actually cold, hence not radiating (or radiating very little).
The second point to note is that radiations from stars far away are redshifted as they reach us, and they are likely to be attenuated by dust. Therefore, even if the radiation itself when emitted is visible light, by the time it gets to us it may no longer be. However, there are still many other different spectroscopic techniques that will allow us to 'see' it.