Yes! A new power supply will definitely fix the stuck mission.  But... It must be larger than 1000w and it must be chrome plated with purple lights.   Otherwise, there's not much chance of it helping.  
 
Running through the Silver Shroud missions, I was chasing down that sniveling coward Northy when I came into visual contact with what appeared to be an Eyebot brawling with a modified Protectron.   Me and MacReady sat back, had a smoke and watched the fight.  Both robots must really suck because they didn't appear to be hitting each other all that much or doing much damage.  So once we got bored, we headed on our way.  There was someone needing a bullet in their skull.
 
Yeah, I knew what the robots were, but I've got enough unfinished missions at the moment to add more to that list. 
 
 

stalinx20
 
I'm right there with you. After I RMA'd the first time with the 1st PSU, after it just "died" while taking out the motherboard along with it, I installed the second one, and this one, after pushing the power button, a gunshot went off, which was a capacitor, so now I have to RMA again... I had bad luck last year.

Gunshot describes it well. The case lights didn't come on so hopefully nothing else was affected.

Knock on wood, I've only had one PSU die on me.  That was my old Ultra 600w (back in the days when a 600w PSU was HUGE) and it just went quietly.  
 
I've actually got several backup PSU's kicking around should anything like that happen.   Though if I lose the power supply in the upcoming WC build I would be stuck with a downed computer as the backups wouldn't be big enough.  

Dukman
Knock on wood, I've only had one PSU die on me.  That was my old Ultra 600w (back in the days when a 600w PSU was HUGE) and it just went quietly.  
 
I've actually got several backup PSU's kicking around should anything like that happen.   Though if I lose the power supply in the upcoming WC build I would be stuck with a downed computer as the backups wouldn't be big enough.  

The only PSU I had explode on me was a misrepresented DiabloTek RPM 1050 that wasn't 1050 watts but a relabled 500 watts PSU. I powered up with a Sapphire HD5870 and a GTX-570 for a PhysX board and it blew up. They sent me another piece of garbage in a plain box with the cables all tangled. It'll power a old low powered Q6600 but that's pushing it.

Zuhl3156

Dukman
Knock on wood, I've only had one PSU die on me.  That was my old Ultra 600w (back in the days when a 600w PSU was HUGE) and it just went quietly.  
 
I've actually got several backup PSU's kicking around should anything like that happen.   Though if I lose the power supply in the upcoming WC build I would be stuck with a downed computer as the backups wouldn't be big enough.  

The only PSU I had explode on me was a misrepresented DiabloTek RPM 1050 that wasn't 1050 watts but a relabled 500 watts PSU. I powered up with a Sapphire HD5870 and a GTX-570 for a PhysX board and it blew up. They sent me another piece of garbage in a plain box with the cables all tangled. It'll power a old low powered Q6600 but that's pushing it.

 
Was an EVGA 1300 G2 which I need to RMA. I have a second one which is currently running this rig.

EVGA's PSUs scare me. I see to many horror stories here at the forum and bad reviews at NewEgg.

My 1300 G2 has been trouble free. 
 
The problem is, we're only seeing/hearing about the few dozens that are bad.  You'll rarely ever see anything about the hundreds that are good.    But I think it also depends on which EVGA PSU you get, because they come from different manufactuers.   Or at least they used to.  
 

OK, I finally broke down and deleted the local content. I'll be reinstalling in about another hour and fourty minutes when the download finally finishes. I hope this works and I don't have to do the same thing with my main PC whenever I get a replacement PSU for it.

Well, that didn't work and was a perfectly good waste of 2 hours. Maybe if I delete some of the saves I might get rid of that stuck mission. Every time I go to the Cambridge Police Station for another tech recovery mission that guy Rhys gets snotty with me for not completing his assignment. I hope he gets over it sometime soon. He never goes outside or I would pick him off with my Gauss Sniper Rifle from a distance.

Zuhl3156
Well, that didn't work and was a perfectly good waste of 2 hours. Maybe if I delete some of the saves I might get rid of that stuck mission. Every time I go to the Cambridge Police Station for another tech recovery mission that guy Rhys gets snotty with me for not completing his assignment. I hope he gets over it sometime soon. He never goes outside or I would pick him off with my Gauss Sniper Rifle from a distance.

blow a cap mine and/or shoot him in the face.