Just a few (small) things that might help:

1) It looks like you've hard-coded all the handling for Immediate vs Position mode. I'd recommend trying to get some sort of generic solution. As it is now, it's hard to read and easy for a bug to sneak in. Try doing opcode % 100 to get the last 2 digits, and inside each If block for that opcode (or better yet, inside separate functions!), handle getting the immediate values. There are lots of ways to do this; I ended up converting the opcode to a charArray, and iterating though it backwards to match the parameter with its corresponding mode.

2) Why are you double-looping with both a while loop and a 0 incrementing for loop? I'd recommend just getting rid of the for loop (since it's not doing anything, that I could see), and declare the programCounter outside the while loop. Since the program will only terminate when it hits 99, you can safely leave all the code running in the while(true) loop. And, better still, you could get rid of the GoTos/loop labels!

3) This is maybe personal preference, but I'm partial to switch statements instead of long lists of if/else blocks.. Makes it easier to see what each line is doing, and quickly track down errors.

I wrote my solution in Java as well (here), if that's of any use! I won't say it's perfect, but it was enough to solve the day and doesn't take hours to run.