In regards to instruments in the church, what about singing songs without instruments outside of the worship service? I have friends who believe this to be wrong. If they hear someone singing along with an instrument or any accompaniment they will walk out of the room. I have been told that God does not like instruments playing songs using his name.
I am a hard-line conservative when it comes to the use of instruments of music in the worship. I prefer to use the argument that instruments were part of the Old Law, and as such are a shadow of the new, and no longer necessary. Why pay attention to the shadow when you have the substance? The other compelling argument to me is that instruments were not used, although available, for at least three hundred years after the church began. (The main reason for this was that the Jews did not use instruments in synagogue because they were part of the Temple worship.) I have never been convinced by the "argument from silence," that the word "sing" necessarily precludes the use of instruments. [This added after the original answer: Nevertheless, as I see people misquoting that argument, the more I find it compelling in opposition to the use of musical instruments, in the assembly of the church.]
Based on the above, I can find no New Testament scripture that specifically forbids singing with an instrumental accompaniment, either in or out of the assembly. I have seen inconsistencies among the brotherhood on your specific question. For instance, I have known an otherwise conservative congregation play recordings of songs before or during the assembly. They would object to singing with an instrumental accompaniment, but not to a mechanical tape player accompanying song if the singers on the tape had no instrumental accompaniment. Others would object, saying the tape itself was a mechanical instrument. I have seen congregations that would object to a guitar or drums, but not to clapping (which is essentially the equivalent of drums). So even among those who firmly oppose the use of instruments there is no agreement.
With that in mind, I would again say that I find no scripture that would prevent someone singing a hymn when they heard it on the radio (or at a "concert") if it was accompanied by musical instruments. Nor do I find any scripture that would allow it. I find no scripture that would prevent someone from learning the tune to a hymn by picking it out on a piano, nor to compose a hymn on a piano or computer. In other words, the scriptures appear to be silent either way. There are, no doubt, some who would disagree with me and object to singing to any instrumental accompaniment of any sort at any time.