Here’s the issue. As soon as you lay out your requirements—FullHD IPS, no optical drive, an SSD, and integrated graphics—which is a perfectly logical setup for business use—it turns out to be a total mission impossible in the US market. In a more sophisticated, larger market, if you couldn't find that exact combo, you could at least step in and upgrade the laptop to your desired specs. But here? Not happening.
The closest thing to what you actually want would be the HP Pavilion, though it's a bit pricey:
http://www.bhphotovideo.com/c/product/example_link_13116Otherwise, the next best things are these two, but they lack an IPS panel:
http://www.bhphotovideo.com/c/product/example_link_13193http://www.bhphotovideo.com/c/product/example_link_13112Then there's this option with a Dell Inspiron 15, where you'd need to swap the optical drive for an SSD:
http://www.bhphotovideo.com/c/product/example_link_13313If I were buying a laptop for myself, I’d go with this Dell Latitude:
http://www.bhphotovideo.com/c/product/example_link_13115It's a genuinely great machine, and honestly, the processor is plenty capable of handling everything you listed. You'd just need to swap the HDD for an SSD and bump up the RAM. That's a slight pain because there aren't any service hatches on the bottom.
So, to avoid voiding the warranty, you'll have to take it to an authorized service center. Since it's only priced around $800, you've got plenty of room in your budget to add another 4GB (or more) of memory and a decent 240/250GB SSD while still staying under your target price... And once you pay the service shop...
You end up with an excellent, ruggedly built laptop that weighs only about 4.4 lbs and gets nearly 8 hours of battery life, all backed by a 3-year warranty and NMWT during the first year (once you register for it). Plus, it hits every single spec you mentioned in your opening post...
You won't find better than that.