My IPhone will not connect to multiple computers

I got an IPhone last October and a new computer for Christmas. I downloaded all my songs to the other computer and have mostly been using it. My IPhone will no longer connect to my home computer. I need to remove pictures from my IPhone that I added to it from the home computer. I cannot take them off on the new computer and it will not connect to the original one. Can I fix this problem without restoring my phone?