Here is a site that discusses some of what could be your problem.

Noisy GE Washers Repair Guide

I think the transmission is the likely candidate, which would mean a new machine given the age of yours and the cost of a fix.

Before you do that, however, you should remove the front and operate the machine to see if you can pinpoint where the noise and problem is.

I understand the issue of the cost of a new machine. Look, a basic, no frills top loading machine will do a fine job and not cost too much, so I recommend that.

Also, in our area a very good used machine can be had for about $100 to $150.00, and if it is a top loader you should do fine.

Good luck