Without the model of television, I'll have to make some assumptions in order to answer your question.

Primarily, most newer televisions of this size are either LCD or DLP projection televisions. And in both cases, if you receive "no image," chances are high that your projection bulb has gone out and will need to be replaced.

Replacement bulbs range in cost from $250-$500 depending on the bulb.

You will want to contact a service center to verify that the bulb is the problem, and then either have the service center replace it (if it is not user serviceable) or order a replacement bulb and replace it yourself (if it is user serviceable.) Either way, you'll want to be in contact with a service center before replacing the bulb, as if it is NOT the bulb, the bulb will NOT be returnable once it has been installed in a television.

This is the community Q&A board, so you are speaking/asking other consumers. I'm not aware of Best Buy doing any type of electronics repair. Their extended warranties/etc are actually handled by third parties.

Unfortunately, where you've asked the question is actually the "community Q&A," so you're actully asking other consumers. You would probably have to contact Best Buy's Corporate Office in order to obtain this type of information.

This would depend on the type of Audio/Video you are trying to split.

Splitting Composite Video : (Yellow/Red/White connections) VERY simple. You don't need a device, ... you can buy three RCA splitters at any electronics store for this. (Cheap)

Splitting Component Video :
(Red/Green/Blue/White/Red) Same instructions as above, except you will need FIVE RCA splitters. (Cheap)

Where it gets sticky is with HDMI. You "can" split HDMI, but you have to have a device specifically designed to split HDMI, ... and they are VERY VERY VERY expensive. The reason for this is that HDMI data streams are designed (for DRM purposes (Digital Rights Management)) to authenticate the device on the other end. The device won't output anything over HDMI until the display/device is authenticated. So, ... you can't attach two devices to any type of HDMI cable splitter, or two devices will try to sync at the same time and it will simply fail. An HDMI splitter is a device that authenticates as itself and plays "middle-man." It then authenticated with the display(s) and forwards digital packets to them... The last time I recall seeing one, I believe it was in the $2000 range.

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Based on your question, this could mean the other way around, too. (How to receive multiple inputs to one device without an audio receiver, when the television doesn't have enough inputs.) In which case, Best Buy sells a "gaming" A/V switch box as well as an HDMI switch box. The gaming switch box can be found in the PS3/XBox area, and the HDMI switch box can be found in the home theater dept, and sometimes, right next to the gaming switch box as well..