How do I load wallet.dat on new PC and import everything into Electrum? My primary PC died last month due to what I believe is a motherboard error. My EVGA board displays "FF". The fans, drives, everything powers up as usual. But I don't hear any beep, no POST, no BIOS, just nothing.

Since then I've taken up residence on a box much more modest than what I'm used to, but I've used it as an opportunity to learn Linux. Nothing like jumping in head first.

Luckily I have a backup wallet.dat file taken at some point after my last known transaction. I changed the filename of the file in the directory, then renamed my backup as wallet.dat and loaded up Bitcoin Core on Linux Mint 13 Maya.

It was partially successful. I could view and export a list of every transaction I've ever made with my desktop wallet. I opened my CSV file in Calc and found the total sum of transactions left the balance equal to what I remember last having in the wallet.

However, the wallet has no balance and all the transactions have a "conflicted" status. Do I need to download the blockchain first? Is it worth my time to download bootstrap.dat?

After my funds are accessible in Bitcoin Core, how do I then move them to Electrum?
You can also import the wallet.dat directly into Electrum. Bitcoin Core needs to download the whole chain (as you mentioned) so that'll take a while. Without the chain, your transaction are indeed illegal/conflicted. Since you have the wallet, you can just install Electrum and import it there. Electrum doesn't need to download the chain, so your balance would be visible (and accessible, even more important) immediately.