I start off most answers with the fact that I know most questions are months to over a year old, but at least someone might get an answer if they have a similar issue! :)
#1 Right off the bat, it sounds like your battery is toast...this is even more likely if its quite a few years old(some batteries are good for 3 years, others, 5-6+...If you can see a date of manufacture on it and that date is less than the warranty period, take it to wherever that battery is sold to get it tested and possibly replaced under warranty!
#2 Check out Rockauto.com for parts, they had parts for out T/Ts (Tempo's/Topaz's) that I couldn't find ANYWHERE ELSE!!! Plus they ship worldwide, (decent enough shipping rates to Canada, factoring in the price of the same parts up north here...lol, if you order enough things to makeup for the sometimes higher international shipping) and just awesome rates to the US regardless of what you order! :)
#3 Back to the battery info... Anyone can get their battery tested for FREE at just about any shop, Autozone, Napa, etc... I tell people to get two, three or more free opinions on anything car related because I often get people asking "Well won't a shop just try to sell me something I don't need? My answer is simple, not if you steer clear of most chain places... Many independent shops will bend over backwards for your business, and most can't afford to lose customers like chains can, so honesty and repeat customers are KEY! (So, if you think a shop is going to bother trying to falsely sell you a battery when yours is fine, that's a bit of a stretch in most cases...have them walk you through the test process and explain WHY your battery is either OK, or is history...),have them show you the reading(s) to prove it if you doubt their honesty at all or have an inclined buddy bust out his multimeter and test it himself!!
Google "battery runs down" for HUGE amounts of info as to what the issue may be!
The following site has some useful info if you don't want to "take a stranger's word", you can know what's correct and what's not for yourself... but overall, (battery wise), most places are pretty genuine...as they want repeat customers, not walkouts...its simple, if you don't feel right at a shop, leave, there's many more!
http://www.aa1car.com/library/battery_runs_down.htm
#4 Yes, a corroded wire harness can cause unfathomable electrical headaches, look into getting a new connector and then having it spliced in properly, or before going to the trouble, try and clean it up with a NON-metallic abrasive brush and some WD-40 (don't want ANY sparks near the tank), ask a pro how to clean it if you're unsure in ANY way!!
~Matt