The company I work for does not allow personal computers on the network. It’s viewed as a breach of network security. Personally, if I find myself in your situation, I would make the case that the computer provided to me is not up to standard and will impede my productivity, and request a new machine.

I wouldn’t recommend using your personal computer for work regardless. If you want to install stuff on your own machine, for instance, you don’t want to have to worry about how it’s going to affect your work.

To expand a bit on my comment on @KateGregory’s answer, the problem you face with using your own computer is “who owns what?”. How is a line drawn between things that you do on that computer for the company vs. for yourself? If you work on other projects off the clock, can the company make any claim to those? Does the computer have to comply with all corporate standards & policies, including antivirus, web filtering, remote scanning for unapproved software, etc.? Who owns the software you’re using? Who’s responsible for the licensing?

You are going to have to wait a couple weeks before you can make any kind of pitch to get a usable computer. Otherwise, you come across as the new guy who wants everything “just so”, and that will not earn you any points.