You could do something like this:
COUGAR Spike Black Steel / Plastic MicroATX Mini Tower Gaming Case with USB 3.0 and 12CM Cougar Fan
Model #: Spike
Item #: N82E16811553011
$36.99 -$7.00 Instant $29.99
ASUS H81M-E LGA 1150 Intel H81 SATA 6Gb/s USB 3.0 Micro ATX Intel Motherboard
Model #: H81M-E
Item #: N82E16813132042
$60.00 -$3.00 Instant $57.00
MSI R7 260 1GD5 OC 1GB 128-Bit GDDR5 PCI Express 3.0 x16 HDCP Ready CrossFireX Support Video Card
Model #: R7 260 1GD5 OC
Item #: N82E16814127780
Mail in Rebate Card
$99.99 $99.99
Antec VP-450 450W ATX 12V v2.3 Power Supply - Intel Haswell Fully Compatible
Model #: VP-450
Item #: N82E16817371045
Mail in Rebate Card
$49.99 -$12.00 Instant $37.99
Intel Core i3-4130 Haswell Dual-Core 3.4GHz LGA 1150 54W Desktop Processor Intel HD Graphics 4400 BX80646I34130
Model #: BX80646I34130
Item #: N82E16819116946
$119.99 $119.99
G.SKILL 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10600) Dual Channel Kit Desktop Memory Model F3-10600CL8D-4GBHK
Model #: F3-10600CL8D-4GBHK
Item #:N82E16820231180
$45.99 $45.99
Western Digital WD Blue WD5000AAKX 500GB 16MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive Bare Drive - OEM
Model #: WD5000AAKX
Item #: N82E16822136769
$59.99 -$10.00 Instant $49.99
Subtotal: $440.94
There a couple of rebates in there, but some items will have shipping charges. $420 is a very tough budget to hit. Hopefully it has a little wiggle room in it.
Edit: You'll want to recheck pricing though; another i3 may be cheaper right now, and I've seen some good video card deals in that range for something stronger, or a little less for the same GPU. RAM too, could be a few bucks less. This time of year, expect significant deals.