Welcome, nice choice for first pinball. Let's give you a few first pointers and a few links....

The 5 "bomb dropping" noises and the ding are OK. If the display was working, you'd be seeing an error message about Factory Settings being restored, which is because the batteries are missing. The correct action then is to press the button in the coin door, which resets things and lets you continue. If the batteries were in place, you'd only get that first time around.

So - yes, the machine will run without batteries, but you'll need to get through the factory settings message each time before you can play.

The 5 flashes you originally were telling you that U41 was bad (probably from the battery corrosion looking at the picture), so nice job replacing it. Continuous flashing is what it should do if it's running properly.

For the power supply, as usual check the fuses. The power supply board is the one top right inside the backbox, check all the fuses there. It's not uncommon for the high voltage section for the display to blow on an old machine, so if you replace a fuse and it blows again it'll need some more looking at.

Some more resources which you'll find invaluable.....

IPDB (internet pinball database). The F-14 page is here, you can download a copy of the manual with schematics if you don't have one already.....

http://ipdb.org/machine.cgi?id=804

Pinwiki. This is a constantly growing collection of information on repairing and maintaining pinball. This is the link to the section relevant for F14 (which is a "system 11" pinball).

http://www.pinwiki.com/wiki/index.php?title=Williams_System_9_-_11

Pinrepair. This was originally "the" place to go for repair information. The site was taken down a few years back as the information was getting outdated, and also because pinwiki was up and coming. There are a few mirrors kicking around though, this is one of them. Some links are possibly broken, but still worth nosing around.

http://techniek.flipperwinkel.nl/wms11/index1.html

Feel free to post away with more questions, we're a friendly bunch (mostly!)

Mark

Disconnect all the cables from the display, replace the fuse again and power up. If it blows again it's the power supply. If not, it's the display (probably).

You have another couple of options for fixing. The high voltage section is prone to blowing in an old machine. A number of vendors sell kits containing just the components you need to rebuild it. Given you're obviously handy with a soldering iron, should be an easy 'tinker'. Less than $4. Worth a go.

https://www.greatplainselectronics.com/proddetail.asp?prod=wan-hvp-kit

Replacing the power supply with a more modern version is also an option, as you suggest. The final more expensive option is to replace all the displays with LED versions, lots of vendors for those. They don't require the high voltage supply and run from the 5v (and some 12v) in the machine. If you fit those, you can remove the 100v fuses. You're likely looking around $200 for new displays though, so the other options are cheaper.

If you're just wanting to see if the power supply will blow with the display disconnected, you can use the 1/2 amp. If the power supply is bad, it'll probably blow the 1/2 amp too. Those breakers are cool though, one of the things that you don't need very often but are great when you're trying to dig around a knotty problem.