In my experience it's worth giving them a call rather than going through the online chat. Each vendor is different, sometimes the online chat is better, but with them not being particularly helpful I would be inclined to call.
We don't deal with HP directly, we use a distributor for our IT, not to mention we're in different countries, so I can't really tell you from experience whether they're likely to offer free shipping or not. Worth a phone call though
remember you'll be calling a sales team, not tech support, so you're less likely to get put through to India/Pakistan/Timbuktu.
A tip, just make it clear that if they're not competitive they will lose the sale to a competitor. It really will depend on their targets, figures, and a hundred other things, but you may well be able to negotiate a discount and/or free shipping.