You can get a new third party battery fairly cheap on eBay. Every MacBook from 2006 through Mid 2009 except the Late 2008 Aluminum Unibody and the Late 2009 and 2010 White Unibodies use the same A1185 battery.
Black Batteries http://shop.ebay.com/i.html?_nkw=macbook+black+battery&_sacat=0&LH_BIN=1&_sop=12 &_dmpt=Laptop_Batteries&_odkw=macbook+white+battery&_osacat=0&_trksid=p3286.c0. m 270.l1313
White Batteries http://shop.ebay.com/i.html?_nkw=macbook+white+battery&_sacat=0&LH_BIN=1&_sop=12 &_dmpt=Laptop_Batteries&_odkw=macbook+black+battery&_osacat=0&_trksid=p3286.c0. m 270.l1313
Or for $129 from The Apple Store http://store.apple.com/us/product/MA566LL/A?mco=MTY3ODQ5OTY
The 10.6 Snow Leopard DVD is back in the Apple online store. You can get it for $19.99. You will need to be running 10.6.8 to access the App Store to order Lion. http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard
Once you are at 10.6.8 Lion is still available from Apple. You will have to call Apple Customer Care 1-800-692-7753 or 1-800-676-2775. to purchase it. Then within 3 days you will get an email with a code which you can use to download Lion from the App Store. The price is $19.99.
Lion will require at least 2gb of RAM but really needs 4gb to run smoothly.
As for third party programs see this list for compatibility with 10.7 http://roaringapps.com/apps:table
Also Lion doesn't run any Power PC programs. To see if you have any Power PC programs go to the Apple in the upper left corner and select About This Mac, then click on More Info. When System Profiler comes up select Applications under Software. Then look under Kind to see if any of your applications are listed as Power PC. Universal and Intel will run under Lion.
Before Mac switched to Intel processors in 2006 they used Power PC processors from 1994 to 2005. Power PC 601 through 604, G3, G4 and G5. Applications written for the Power PC processors need the application called Rosetta to run on Intel processors. This was part of the Operating System in 10.4 and 10.5 but was an optional install in 10.6. With 10.7 Lion Apple dropped all support for Power PC applications.