If the washer will not drain, the drain pump is the logical place to look. I would hope the servicer at least opened the sump assembly and cleaned it out before giving you an estimate. The pump is not the easiest thing to replace, but neither is anything else in your washer. I would first verify you have voltage going to the pump to be sure this isn't a control problem and clean out the sump (be ready for water because anything in the tub will be in your lap very quickly) before I did much else. And yes you will find parts prices (especially on line) much less then servicers will charge when visiting your home. In some cases, they are probably just trying to get the service fee and trying to get out of the home quickly, but when a part is replaced by a service company, they are assuming the liability for the cost and warranty so reasonable markups should be expected. Start with checking the sump and see if you find anything. Then if you need to replace the pump, get a set of star bits for your screwdriver and have some towels handy.

Yes you would need a multimeter to test voltage and if you already drained the pump, then you are down to the pump or board being the problem. I am not surprised by an inflated estimate as this is a tool used by some servicers to get out of work. They basically don't want to repair your appliance, but instead want your go away money often called a trip charge. If it looks like the appliance is going to need much work and they would need to return with the part, they just inflate the estimate so you decline it and they move on with your $50 in hand. We have several servicers in my area that basically set their trip charge at a level to be profitable and if the call is anything like yours, then they get paid and never really need to do any work. I don't like it myself, and although these guys are usually what I consider poor technicians, they still get business from unsuspecting consumers. You can try the pump if you want to, or check for voltage first, or go with another servicer. Whichever way you go, you are probably going to spend less and still get it repaired.