A TV would work as a monitor as long as the TV has HDMI/DVI ports on it.
So here's one without a monitor included:
PCPartPicker part list:
http://pcpartpicker.com/p/22GpL
Price breakdown by merchant: http://pcpartpicker.com/p/22GpL/by_merchant/
Benchmarks: http://pcpartpicker.com/p/22GpL/benchmarks/
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($117.97 @ SuperBiiz)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.98 @ OutletPC)
Motherboard: Asus M5A97 R2.0 ATX AM3+ Motherboard ($94.99 @ Amazon)
Memory: Crucial Ballistix 8GB (2 x 4GB) DDR3-1600 Memory ($69.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.98 @ OutletPC)
Video Card: XFX Radeon HD 6670 1GB Video Card ($57.98 @ Newegg)
Power Supply: Corsair CX 500W 80+ Bronze Certified Semi-Modular ATX Power Supply ($49.99 @ Microcenter)
Optical Drive: LG GH24NS95 DVD/CD Writer ($15.99 @ Microcenter)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.00 @ Amazon)
Keyboard: Microsoft Keyboard 200 Wired Standard Keyboard ($7.89 @ B&H)
Mouse: V7 M30P20-7N Wired Optical Mouse ($4.72 @ Amazon)
Total: $598.48
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-15 09:33 EST-0500)