If it's still running Windows 7, there are a few services and such you can disable to try to get it running faster. I've Googled for these before, don't remember where to find them now. I'll note though that I tried all this once and it didn't seem to make that much of a difference.
The better option: install Xubuntu or Lubuntu on it. You can install YNAB on Linux, but it will be difficult. The trick is to install Adobe AIR which isn't supported on Linux anymore, but old versions exist that you can still install manually. Ask if you need help, I've done it once or twice before.