I've always dreamed of building up a light fixed bike too - great for hill climb TTs.

I think the cheapest way to do it is

An unpainted alloy frame
Easton SL forks
FSA ORBIT X W headset
American Classic 24 hole front hub
Campagnolo Super Record 24 hole rear hub
Sapim CX Ray spokes
Nisi Pista Speciali rims
Panaracer Ultima tyres
Outland Carbon seatpost
Selle Italia SLR Flow seat
TA titanium bottom bracket (109mm)
Tune 165mm cranks
TA 3/32 chainring
Euro-Asia Imports Alloy 3/32 cog
KMC 9-speed width chain
Campagnolo Super Record pedals/clips
3T Less bars
Syntace 99 stem

By shopping around you could do this build under £1,000 (pounds, not dollars, sorry)