Bought the geforce 670, windows install crashes

You need a Z77/Z68 board running socket 1155 for that cpu.

Here's a good board:
http://www.newegg.ca/Product/Product.aspx?Item=N82E1681...

Indeed, the new motherboard and CPU doesn't fit together...

however, the "technician" is wrong for saying that the motherboard is too weak! Also when I see what he recommended (motherboard & CPU), to me spells pseudo-technician (that is why I wrote it in caveats)...

The motherboard has nothing to do with "strength to support the GPU"; that statement is out of place...
if he said that the CPU is not up to the task to service the GPU, than he could have a correct argument;

so my answers:

1) No they are not compatible; on their own, they are good choices, but unfortunately they don't fit together; you'll have to find more suitable combination (change either the motherboard or the CPU); the proposed motherboard from amuffin is a good choice, though I would also check the Asus and Asrock as well; also if you chose to go with 2600K, search for a overclocking friendly motherboard - it will be shame not to overclock that 2600K  
future? that is a difficult one when buying computers (hardware);

2) Most likely the cause for install to crash was that the old PSU was some rubbish; But the new one is very good one and if you can afford it, you should not hesitate; though for your setup is a bit of overkill... I have the previous version of that one and it serves me well for 4+ years and it drives overclocked system (check the specs in my profile)

3) No, but is highly advisable! More fans > more airflow > better cooling > longer component life... ut if you overclock, more fans are must!

So in general, you still have some work to do around that computer...  

will either one of these processors work with the motherboard?

Intel Core i7-3820 Sandy Bridge-E 3.6GHz (3.8GHz Turbo Boost) LGA 2011 130W Quad-Core Desktop Processor BX80619i73820
http://www.newegg.ca/Product/Product.aspx?Item=N82E1681...

Intel Core i7-3770K Ivy Bridge 3.5GHz (3.9GHz Turbo) LGA 1155 77W Quad-Core Desktop Processor Intel HD Graphics 4000 BX80637I73770K
http://www.newegg.ca/Product/Product.aspx?Item=N82E1681...

Only the i7-3820 will work - it is the same socket: LGA2011;

when you match processor to a motherboard, look @ the socked info: i7-3820 goes on any motherboadr that has LGA2011; i7-3770K goes on any motherboard with socket LGA1155

Nope.

huh?