No. 1.5 Mbps is still slow for data transfer inside a pc. Take your budget and then look at what you want your computer to do (gaming, office applications) and build the best pc to support your intended applications. Anything you buy today should easily support broadband internet speeds.
No, not really. Your internet speed is a limitation for how quickly you can send and receive internet stuff. Any modern low end computer is capable of keeping up with an internet connection (as ss202sl, the stuff inside the computer moves data much faster).
Do you need additional help selecting PC parts or buying a PC from a vendor like Dell or HP? If so, check out this thread http://www.tomshardware.com/forum/353572-31-build-upgra... and repost with the template in there (you can skip some of the technical questions if you don't know what they mean).
Be sure to clarify what you mean by "video a lot" that can mean anything from simple skyping to editing massive videos or a number of other things and could be important in the advice you get.
edit: Also be aware that building a high performance computer won't let you stream videos any faster than your current computer (unless it's 10+ years old) because that is limited by your internet connection, which isn't very fast. If streaming is your main concern, you are better off trying to find another ISP in your area, such as AT&T or other DSL, or Wireless (either by rural internet towers, or by 3g/4g cellular data plans (but those limit how much data you can use, not exactly ideal).
The video resolution is moving towards 1080p , this require massive amount of data transfer. at 1.5 mb speed u will be able to watch online videos like youtube etc at a medium (?) or lower resolutions without any lag. As ur only concern is watching videos, buy a laptop not a desktop. For wide -screen buy a extra 1080p monitor which r pretty cheap now. Connect it to the laptop (vga or hdmi port) while watching movies or if u have a big tv u can connect to that . For watching movies u wont need a very powerful laptop. Intel + nvidia/amd graphic (note) based laptop will be fine. Avoid laptop with only intel's integrated graphic chip.
It's probably best to simply post the follow up here rather than start another thread (if you see this before you post).
The specs there look like a very powerful machine, and your right they are probably overkill. If it's just a general use internet/email/office computer, any i3 processor, 4GB of RAM, and a 1TB HDD (unless you feel you need lots of storage, try to keep a 7200RPM drive though as that does make a difference).
As long as you aren't playing any games, you don't need a 'real' video card, the Intel HD 4000 graphics are plenty for general use.
These days, computers are quite fast, even the low end parts; because Windows isn't getting significantly harder to run, while the hardware is getting much faster all the time.