Forget about the glow plugs for now, if everything else is wired in correctly and immobilizer is happy the car will readily start and run without them in anything but the most frigid temperatures.... Not likely in August. That's not what's preventing the car from running.
Given your description of the situation it sounds like the electrical system transfer was not done completely. Do you have wiring diagram for both the donor vehicle and recipient shell? What year is the Golf you are installing the parts into? And give more details on the donor vehicle as well -- there is no such thing as a 2001 TDI PD in North America, although they did have them in Europe as early as 01 IIRC. If your TDI donor was a 2001 that would make it an ALH, which is the series before the PD and a whole different technology suite. If it's a PD in a Mk4 car it would have to be a 2004 or later (BEW). These details all matter in terms of what it will take to make it work. Even different years of the same engine code can have significant electrical differences, for example a 2001 vs a 2002 ALH is a different animal with several electrical incompatibilities.
In a vehicle like this you can't get away with halfway-hacking the electrical system together and expect everything (or anything) to function. Need it to be complete and fully functional. Bypassing relays and such won't lead to success. It's easy enough to get it assembled correctly anyway and will save massive headache. Best move would be to cease trying to get it to run using workarounds, and instead focus on ensuring the conversion has been fully executed. Once you have the details sorted it'll run without any struggle. Bolting the physical parts in is no challenge as you already know. The devil will be in the details of making the electrical configuration work. Just plugging in the connectors to the right color locations may not be enough. Depending on how the donor and recipient vehicle match up, you may need a different wiring harness and to make changes on the chassis side.
Do you have VCDS or another specialized VAG capable diagnostic platform? You NEED that to know what issues are occurring and give direction on what to pursue. A scan of engine controller will tell you what the reason is for why it's not running. If no communication, then there's your first issue to go after.