I had a temporary issue with my power equipment not working either (windows, locks, the button causing the "buzz" like you mentioned). My car was also having "hard start" issues.

I also noticed that you said you gave somebody a jump a while back. This may seem really obvious, but you didn't mention it in your post. Have you checked your battery terminals and made sure all the connectors are tightened down properly. Perhaps something was jarred loose slightly from the jump?

Anyways, I was able to find my problem was due to my positive terminal being very loose. As soon as I tightened it down, it resoved all my issues, (power equipment, no more button "buzzing", etc.) My car starts up perfectly now as well, with no hard start issues.

As the others have mentioned though, it could possibly be an ECU. Could be a wiring issue somewhere too I suppose. Start out with the small stuff though, like you've been doing, then work your way up from there. Unfortunately, our cars have a horrible electrical system, quite a shame really, since Mitsu is considered one of the "leaders", in electronics.