2003 Lexus IS300 - Acceleration / Electrical Issue

I'll try to be as succinct as possible.

The Car : 2003 / IS300 / approximately 90K miles / Excellent Condition
The Issues : Acceleration / Electrical
Transmission : Manual / Stick Shift

My Lexus is in excellent condition - truly not an overstatement in the least. It's been in an indoor garage at home and another at work. Unfortunately, because I now have a second vehicle I haven't driven it much at all; save the weekly spin around the neighborhood to keep the battery charged and the parts from getting "stiff".

In October, I went away for two weeks and when I came back the battery was dead. I bought a portable PEAK Jump Starter (900 AMPS), which I believe blew the main fuse (more on that later). Fast Forward >> went to Lexus and purchased a new battery - car starts, but only some electrical components are working : cabin light, door sill lights, headlights.

The remaining electrical components will not turn on - A/C, GPS (OEM), radio, tail lights, et cetera. To make matters worse, the gauges are not working either - fuel, RPM, speedometer, et cetera. I am pretty sure that this has to do with the fact my the main fuse is shot. Is there a DIY on how to switch out the fuses? What fuse(s) do I need to buy?

More importantly, something seems to be terribly wrong with acceleration; it's not nearly as responsive as it was before my battery died. In fact, I need to press down on the pedal halfway before the engine revs. This has never happened before and didn't happen until just after the battery died. Therefore, I'm convinced that something must have happened when I jumped the car.

Is acceleration an electrical function? In other words, could the fact the main fuse is blown be the reason acceleration is not as responsive? I apologize if this is such a naive question, but this is my last resort before towing my car to the Lexus Dealership (no tail lights). I am willing to pay someone for any guidance on the matter. Seriously.

To offer more color on the situation.

1. I do believe that reverse polarity caused the fuse to blow.
2. I do believe that the charger was left on for just a bit before the error was found.
3. I purchased a new battery at Lexus and installed it myself. Car starts and stays on whereas before, it would turn off when the portable jump starter was detached.

Thank you all for your time. I am on the East Coast (North New Jersey) in the event a reputable mechanic is nearby or someone else wouldn't mind helping me with the matter. I will gladly pay for services.

Regards,
Labelina