Take it to a local Circuit City if you have one. We are authorized repair centers for HP's. If it's bad memory the store will order a new part from HP who overnights it to us. If it's something more complicated we're required to ship it off, but it gets overnighted to HP, is there an average of 1-2 days, then overnighted back to the store. I do about 2-3 a week like this and they're almost always back to the customer within about a week. I do once in a while get longer delays, but they're not common.
Deal with HP or Circuit City and not geek squad. I once had a best buy warranty on a laptop. Sent it off to their service center 4 times, an average of 1-2 months gone each time, and they never did get it fixed. One time I sent it off cuz it wouldn't power on. When I picked it up, it STILL wouldn't ><
Oh and no, don't purchase the extended HP warranty, it won't speed the process up any. Like I said, it's actually rather quick already.
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System: Athlon 64 X2 3800+
EVGA Geforce 8600 GTS 256mb PCIE
ECS (pile of crap) Mobo
1.5 GB Corsair PC3200
Soundblaster Audigy Pro
Windows XP Pro, Lemming Optimized.