OP, not sure why the laptop needs to be closed, if you can leave it open, on my Toshiba, pressing the F5 function key connects the external monitor. As noted above you may need a special cable, mine has has both an older VGA port and an HDMI. If you have the owners manual it should tell you how to do this. You can download user manuals if you cannot find yours. Best Buy is probably the best local source for a suitable cable. I am not familiar with a setting that will keep the laptop on with the lid closed, you can select , turn off, sleep, or hibernate. Hope this helps.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
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