Let's see, with actual prices from online stores.
Do bear in mind that this was done with approx 30min of research and you can likely save 100-250$ by optimizing the setup and finding better offers.
Nokia 2760 cellphone, ~65$ with postal http://www.tigerdirect.com/applications/searchtools/item-details.asp?EdpNo=4831707&SRCCODE=PRICEGRABBER&cm_mmc_o=2mHCjCVybgwTyz__wyCjCVqHCjCdwwp&cpncode=19-46747548-2
+20$ for a starter 'pre-paid' connection (includes SIM-card). At least where I live.
eMachines E202HDbmd 20" Widescreen, 110$ http://www.newegg.com/Product/Product.aspx?Item=N82E16824114002
COOLER MASTER Storm Scout ATX Mid Tower Computer Case , 60$ http://www.newegg.com/Product/Product.aspx?Item=N82E16811119196
ASRock M3A770DE AM3 AMD 770 ATX AMD Motherboard , 60$ http://www.newegg.com/Product/Product.aspx?Item=N82E16813157176
Antec EA650 650W PSU (80+ certified), 70$ with rebates http://www.newegg.com/Product/Product.aspx?Item=N82E16817371015
keyboard mouse combo, 68$ http://www.newegg.com/Product/ComboDealDetails.aspx?ItemList=Combo.458390
SATA dvd-driver/burner 20$ http://www.newegg.com/Product/Product.aspx?Item=N82E16827106289
2x2Gb DDR3 1333MHz RAM, 70$ with rebates http://www.newegg.com/Product/Product.aspx?Item=N82E16820227583
SAPPHIRE Radeon HD 5670 (Redwood) 512MB 128-bit DDR5 PCI Express 2.0 x16 HDCP Ready, 90$ http://www.newegg.com/Product/Product.aspx?Item=N82E16814102871
250Gb SATA internal HDD, 47$ http://www.newegg.com/Product/Product.aspx?Item=N82E16822136161
AMD Phenom II X3 720 BE (triple-core 2,8GHz), 100$ http://www.newegg.com/Product/Product.aspx?Item=N82E16819103652&Tpk=phenom%20ii%20x3%20720%20black%20edition
KWORLD ATSC TV Stick USB2.0, 30$ http://www.newegg.com/Product/Product.aspx?Item=N82E16815260023
OS: Linux, downloaded free with a friends computer (for example, Ubuntu-linux).
Total money used: 810$ x1.22 for VAT = 988$. (as I wasn't sure if VAT was included in NewEgg prices, so I took the safe route.)
You get a 20" widescreen LCD, triple-core 2.8GHz (that is easily overclocked what with the unlocked multiplier of the Black Edition), 4Gb of DDR3 RAM, ability to watch TV and DVDs and play games at decent settings. You also get a functional cellphone.
Or, if you wish to get nitpicky, save 20-30 dollars from the cellphone and another 20-30 dollars by searching for better deals on components, and you can buy a basic TV-antenna as well as pay for postal service.