The lines are either a problem with the monitor or the graphics card. Randomly shutting down is a problem with your power supply, either its busted, its not putting out enough watts or there's something wrong with the power/restart buttons. The wires might also have a break in them. It also might be overheating and shutting down as well.
If you built it, then try to find the problem or ask the store to do it for you (assume they have customer support for that) if you bought it from a company pre-made then call there support and get a replacement if its under warranty (this shouldn't happen from store bought).
If you built it, then try to find the problem or ask the store to do it for you (assume they have customer support for that) if you bought it from a company pre-made then call there support and get a replacement if its under warranty (this shouldn't happen from store bought).