Just getting started in KAP after a really long hiatus from tabletop RPG's. I still have my (much-read, never actually played) hardcopy of 3rd edition. I also have .pdf of 5th edition and GPC.

Question... Can I run GPC with 3rd edition rules? Are there any core differences to the rulesets that make them fundamentally incompatible?

I have access to .pdf of 5th edition and don't mind printing a replacement chart here and there..., also I can crib notes from the electronic copy where needed between sessions, but there is really no replacement for a hardcopy when you want to flick through pages to look up a rule on the fly.

It's just that I already have a 3rd edition hardcopy and $100 minimum for a used copy of 5th on ebay is... well, it's something I can afford but it wouldn't be without some pain on my budget.

Help? Thanks?

If you have both 3th edition and 5th, you can quickly compare them to one another. As far as I can tell, the core rules have not changed much. attributes, traits, passions and skills still work the same way. There are some minor differences, like the elimination of Double Feint, but nothing major, iMHO.

The biggest difference is the starting time, since 5th edition starts at 485 (like GPC) and 3rd edition is set in 531. Thus, Romance and Tourney don't exist yet. But since you have 5th edition pdf, you can easily use it for the world information and carry 3th edition with you for the basic rules.

What Morien said.

Since you are keen on paper books, you can get a printed copy of either KAP 5 or 5.1 from Drivethrurpg.com, for 30 $ (softcover) or 35 $ (hardcover):
http://www.drivethrurpg.com/product/3163/King-Arthur-Pendragon-5th-Edition?sb=1&it=1&filters=0_0_44536_0_0
http://www.drivethrurpg.com/product/81449/King-Arthur-Pendragon-Edition-51?sb=1&filters=0_0_44536_0_0

It is print on demand, but the quality of Drivethrurpg is usually high or at least acceptable. KAP 5.1 is almost identical to 5.0, it mainly includes some errata, so I would suggest purchasing 5.1 if you decide you want a paper copy.
Nocturnal has also published the PDF of KAP 5.2 (same system as KAP5, a lot of corrected errata, new layout & graphics), but no printing option is currently available.

3rd and 4th are essentially identical where they overlap; GPC can easily be run by simply using battle in place of siege.

I am currently using 4E+GPC for the 4th time.