Good chance the ECM has put the car in "limp" mode to prevent damage.
Start with getting it scanned even if the CEL isn't staying on. After that it's time to take it to your favorite pro.

 

Sounds like the jumper cables were low quality and/or crossed (polarity) or both. Also, always attach the jumper cable ground clamp, to engine ground not battery ground (see the owners manual). This can produce a spark that can ignite hydrogen fumes from the battery after the car is started. This is more of a safety issue to prevent a battery explosion. I suggest purchasing a good quality set of cables and keeping them in your trunk.
Obviously, I would start by installing a new battery and go from there. If that doesn't resolve the issue, have it diagnosed by a qualified mechanic.

 

he attached both leads to my battery causing it to spark. We quickly detached one and attached it to the frame instead.

Doing so might have damage the ECU, therefore control of the electronics of the vehicle, including "throttle by wire" (sensor for operating gas pedal). Or it might be that the battery is simply too weak for ECU/electronic systems to work properly.

 

you might try removing the negative battery terminal for 10 mins then reattach. Then inspect the ground bolt located under the air box. Clean the ground contact and reattach the ground battery terminal. Ground signals are used to control throttle and idle. Cleaning these terminals normally corrects the issue and removing the battery terminal resets the computer.

 

I've had this experience myself where the jumper cable burned up. A hard reset of the ecu may help, but also check the positive cable for signs of burning.

It sounds to me that the car is in limp mode. Any check engine codes?

 

I had a similar incident happen to my 2011 Camry and the solution was a blown fuse for the electronic throttle control.

 

I experienced same with my vehicle, the engine runs fine, and revs alright but won’t move when accelerated in drive mode. This was resolved when I replaced my battery.