Have you given up on trying to repair it? If you see your way to finding the correct screwdriver bit and a decent soldering iron you might get lucky and find it's a defective 3-terminal triac (one of the components in GRJ's red box) which can be replaced with modest effort/cost.
When you say "budget AC/DC transformer" are you saying your accessories run on DC voltage (most do)? If so, you can find very economical DC output power sources. Note the Tech II Railpower 1400 is spec'd at 13VA which for comparison purpose is 13 Watts which is rather anemic for O-gauge applications.
If you can use DC, here's a 90 Watt supply that goes for between $5-10 shipped on eBay (search for 90W Universal laptop charger). This one has a selector slide switch to change the output voltage from 12 to 24V DC in 7 steps with LED selection indicator.
Note that it's generally much easier to convert from one DC voltage to another DC voltage - vs. AC-to-another AC votlage - for fine-tuning accessories that respond to voltage changes. It's true though that with these low-cost DC supplies (look for 10 cents per Watt or less) from the PC/computer industry you generally have to mess with connectors/wiring whereas a train transformer typically comes with color-coded red/black banana jacks or clearly labeled + and - screw-terminals.