QuickBooks desktop would do a lot of what you want, as others have said.  The reports you could get might even surprise you--like linking customers with repair bills and repair bills with individual machines, etc.

Customer list - easy, pretty automatic, as it would be with any accounting software.

Equipment List - best way to do that would be with Inventory Part Items (the Items list lets you set up an identifier--an "Item"--for each piece of equipment). But you'd really need to understand the Items list. The QuickBooks Farm Accounting Cookbook™ Volume IV, which is about using Items for fixed assets, would help with figuring out how to set up an organize individual equipment Items. Doing that is not entirely simple (sorry).

Note:  books and articles on using QuickBooks for Construction businesses would also apply very well to what you're doing.

Repair Orders & Invoices - use the QuickBooks Sales Orders feature for providing repair quotes, or for keeping track of parts & labor applied to a particular repair. Sales Orders can then be converted to Invoices when you're done with a job.

Part Numbered Inventory - Inventory Part Items would work for that. But understand that *every* inventory system requires more "fiddling with it" to keep it accurate than most people expect at the outset.

If you get painted into a corner and feel the need to use cloud-based software, be sure to check out the inventory features. And I strongly recommend AGAINST QuickBooks Online--it works for some people, but in general it's a turkey for most. 

I've been trying out a cloud-based system called ZarMoney, and am fairly well impressed with it. It is organized more like QuickBooks desktop than QuickBooks Online is! ...which makes it easy for QuickBooks desktop users to get started with. Has a few rough edges, mostly in reporting (for instance, lacks a Cash-basis P&L report...but they are working to add one right now), but has really nice ease-of-use features I didn't expect. And though I detest monthly software subscriptions, at $15/month it is one of the less expensive packages for all it does--MUCH cheaper than QuickBooks Online.

I don't know enough about ZarMoney's inventory features yet to be able to either recommend or disrecommend them.

Mark Wilsdorf
Author of The QuickBooks Farm Accounting Cookbook™ series