You won't find any help at tech support ... other than telling you the facts: Intel processor Macs require FCP 5.1 or higher. FCP 5.0 and earlier were written for PowerPC processor Macs, long before Apple switched to using Intel processors.
And then there's the issue of the OS. OS 7 will allow FCP 7 (and sometimes even FCP 6) to work OK, but versions earlier than that have spotty operation on Lion.
Here's a brief history of full FCP versions and recommended OS compatibility:
* = requires PPC ** = works with both PPC and Intel *** = require Intel
FCP 1.0* OS 9
FCP 2.0* OS 9
FCP 3.0* OS 9, OS 10.1, OS 10.2
FCP 4.0* OS 10.2, 10.3
FCP 4.5* OS 10.3
FCP 5.0* OS 10.3 (OS 10.4?)
FCP 5.1** OS 10.4, 10.5
FCP 6.0** OS 10.4, 10.5, 10.6 (OS 10.7?)
FCP 7.0*** OS 10.6, OS 10.7
FCP-X*** OS 10.6, OS 10.7
Essentially, you have a newer Intel processor Mac with a new OS and very old, incompatible software. You might be able to find a used version of Final Cut Studio 3 on sites like ebay or craigslist as it is no longer offered by Apple as an upgrade.
Alternatively, you could purchase and download FCP-X, but it is an entirely different application, sharing virtually nothing with previous versions of FCP.
-DH