How do I install Photoshop 4 without a disc drive?

do you mean photoshop cs4, not photoshop 4 or photoshop elements 4?

if so, you can expect some (or a lot of) problems if you're using an incompatible (ie, newer) os.  but you can download the installation file(s):

Individual User Downloadable installation files available:

• Suites and Programs:    CC 2017 |  CC 2015.5 | CC 2015 | CC 2014 | CC | CS6 | CS5.5 | CS5 | CS4, CS4 Web Standard | CS3
• Acrobat:  DC, XI, X | X Suite | 9,8 | 9 pro extended exe,9 pro extended 7z | 9 standard  | 8 standard |
• Authorware:  7.01 windows |
• Captivate:  10 (2017) | 9 | 8 | 7 | 6 | 5.5, 5 | 1
• Cold Fusion:  11, 10 | 9.0.2, 9.0.1, 9.0.0, 8.0.1, 8.0.0, 7.0, 6.1, 6.0, 5.0, 4.0 |
• Contribute:  CS5 | CS4, CS3 | 3,2
• FrameMaker:  12, 11, 10, 9, 8, 7.2 |
• Lightroom:    6.10| 5.7.1|  4.4 | 3.6 |
• Photoshop Elements:  15,14,13,12,11,10,9,8 | 9,8,7 win | 8 mac | 7 mac
• Premiere Elements:  15,14,13,12,11,10,9,8| 9, 8, 7 win | 8 mac | 7 mac
• RoboHelp:  2015, 11, 10, 9, 8

Download and installation help for Adobe links

Download and installation help for Prodesigntools links are listed on most linked pages.  They are critical; especially steps 1, 2 and 3.  If you click a link that does not have those steps listed, open a second window using the Lightroom 3 link to see those 'Important Instructions'.

And a big thank you to Jim @ Prodesigntools for helping me with these links!