That's better. I have no idea if an HPD inspector will do anything that is not a violation. They can't say whether something was done, or not, and at what price. You might need an engineer or architect for that - to show the work was not done.
Whatever you do, take many photos showing the old work in place. You can ask for a DHCR inspector. In some cases they might be better than the HPD inspector, especially as to the old work still existing.
I would attack the sufficiency of the LL's documentation. Not a contract could be important. That it's not itemized is a real problem. I would really pound away on that one. What about the check. Were both sides included? Does it match the invoice?
As for DOB filings, it's all on computer these days. In the 90's it was on paper and I don't know if DOB still maintains the paper files. Some larger drawings would have been put on microfiche. If you go to 250 Broadway (I think it's the 3rd floor, but ask when you get there), you can put in a requisition to access various files (look for the yellow cards). You can find the permit or application number on the DOB website (and they don't make it easy).
The clerks are rude and non-compliant in many cases, so you might need to suck-up to them and get help from the professionals (expediters) who are filing their own projects. Many will help to speed you along.
For electrical, construction and plumbing work there has to be application folders and permits. For items like putting new tiles on a floor, no DOB permission is needed.