Newegg.com is a great place to look around and build your dream PC. It lets you put together a wishlist also so it gives you the total cost of all your parts and everything as well.
I'm not going to link specific models for certain parts but just offer some of my suggestions. $2,500 is a good bit of money, and should get you a great system.
CPU: The i7 2600k Sandy Bridge
Motherboard : An ASUS brand motherboard. On Newegg you can sort by CPU type and everything, and just look for one that has the most options that you'd be using. USB 3.0, SATA6, etc.
Video card: I like nVidia myself, the GTX 460/470/480 is a very good card, especially if you've got 2 in SLI. If you've got the spare cash you could always go for 2 of the 500 series cards, but it would be a lot more expensive.
Power Supply: If you plan on SLI or Crossfire you're probably going to want at least a 1,000w PSU from Antec.
RAM: 8 GB of DDR3 RAM can be had for only $100. Corsair is a great brand but tend to be a bit expensive. G.Skill is another great brand and offer a lifetime warranty on memory.
Gamer's Case: I'd go with a Lian-Li aluminum case. They're pricey but are definitely worth it. Newegg also has a sizable selection of cases.
CPU Cooler: I've got a Cooler Master Hyper 212+ air cooler on my i5. It's only $30 and is quite simply one of THE best coolers you can get. I'm not sure if it's compatible with the Sandy Bridge socket type however. I heard from a guy I work with that the mounting holes for the CPU cooler are slightly different than his old i7 so he has to get a new cooler.
Hard drives: Honestly, SSDs are great. An Intel 80gb ran me about $200 before Christmas, and all I have on there is my OS. It boots up SOOO fast and is super responsive. It's clearly the biggest impact upgrade in recent memory. Also you can get a 10k RPM Raptor for putting your games on, since they don't cost quite as much as SSDs. Then something like a 1 or 2TB storage drive for pr0n, etc. etc...
DVD Writer: Anything Plextor. I think I've seriously had my 8x Plextor DVD burner for nearly 10 years now and it's still going strong. Never had any reason to upgrade or replace it.
All you would need to hook up your computer to the TV would be a DVI-HDMI cable. My 24" monitor actually came with one because it doesn't even have a DVI connection, it's HDMI.
20 years of computer experience.
Just did a major upgrade to my own computer before Christmas.