If your looking for absolute cheapest, try the MSI Radeon 2400PRO. I have it and its a fairly nice card. The specs say it is HDMI compatible but I've never tested it yet.

Newegg.com - MSI RX2400PRO-TD256EH Radeon HD 2400PRO Support up to 512M(256MB onboard) 64-bit GDDR2 PCI Express x16 HDCP Ready Video Card - Desktop Graphics / Video Cards

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Intel E4500 Dual Core ~2.2ghz
Radeon 2400PRO ~525Mhz w/ 512mb
Triboot Xp, Vista, and Ubuntu WD 250g