... Interestingly, when I booted the computer with the CPU removed it did the same blinking.
If it's doing the same exact thing with the CPU removed from the motherboard, that might be an indication as to where the problem lies. CPUs are delicate, and it's entirely possible that it got cracked when the system fell/landed. If you remove it from the system and look at the underside (the side with all the copper leads) and notice any cracks, the CPU is shot. If you can't find any noticeable damage, that won't always means it's not damaged - you just can't see it.
As far as the techs go, if you tell them up front that you WILL NOT spend more than $xx on the repair, any reputable shop will still swap out the components until it works, and tell you how much it would cost to keep those parts in the system. If you tell them "no way", they should replace the existing components and only charge you for an hour (or so) of labor.
Aside from that, check the motherboard itself to see if you notice any cracks, blown capacitors, or any other damage to the board. It's very difficult to explain to you what to look for, since I usually don't have to think about it when I do it (yes, I've been doing this for a very long time :)