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1) What will you be using the PC for? Web browsing and word processing, spreadsheet number-crunching, video editing, photo editing, DVD watching, game playing, etc.
2) Will you also be looking for a new monitor, too? If so, is that part of your price range? What size monitor?
3) How important is tech support to you? Would you use it often? Would you pay for a higher level of support and/or an extended time period where you could get support?
5) Why specifically a desktop PC? Are you sure you want a desktop and not a larger laptop?