Research administrator here. It appears that you are accusing the PI of fraud, is that right? Let me explain the proposal and award process roughly for government grants and contracts before we jump to that conclusion, although some PIs do commit fraud. Please note that the sponsor and exact solicitation will vary the rules which I cannot speak to without knowing this information.
When you put in a proposal, you respond to a specific solicitation (RFP/BAA, etc.) that will put forth some rules, potentially what cost categories you can spend on. E.g., with NSF, the MRI program restricts the entire budget to a piece of capital equipment. The REU and RET programs focus on training undergrads or teachers. Some solicitations are very open, and you can propose a budget with "any" cost category.
There are federal restrictions on what government money will fund, however there are exceptions if you put the costs into your proposed budget and the government agrees to fund it. An example would be with studying alcohol. Alcohol as an entertainment expense is not allowed on federal grants, but if you are studying alcohol, it can be cited as having "unlike use" and then you can classify it as a lab supply. Similarly, "office supplies" are not allowed on grants as they are part of the "indirect cost" line (typically ranges from 50-70% of the direct costs), but if you were to propose a project that has a large focus on surveys, it would be reasonable to ask for paper, envelopes, and postage as a direct cost. As for computers, in 2014, the passage of Uniform Guidance changed the rules for charging computers to grants. It used to be that they had to be "sole source", e.g., running a piece of equipment. Now you are allowed to split-code them between multiple projects. However, you still have to meet the burden of determining the allocation. If a computer should be split between 10 funding sources, one could argue that it is similar to an indirect cost, and thus does not belong on any grants. In my computer science department, we do not charge student computers to grants for this reason. We do not want to have to track usage. However, when really fancy computers are purchased, we do budget for them upfront because they are beyond the normal administrative machine for email, etc.
As charges hit the funding, there are research administers who are hired to monitor the spending, and requirements for internal controls mean that audits are periodically performed on expenses. It is very possible that when costs are proposed to a research administrator (like myself) the proposed costs are not considered allowable on the project. The sponsor may have restrictions preventing a rebudget or the exact thing (which appeared to be in the proposal) cannot be purchased for other reasons, e.g. strategic procurement could block an equipment charge. Sometimes I have found conflict of interest problems because the PI wanted to buy equipment from a small business they have too large a stake in and the university blocked it.
It's always possible that the funds are also unspent and not misused. Unless you are privvy to the exact spending, you cannot know how things were spent to know that funds are misused. At the end of the day, the institution will send financial reports to the sponsor, and the PI is responsible for sending annual (or more frequent) technical reports. Are you assuming the technical reports are fraudulent and are falsely reporting progress on the project? Also consider that if your institution has an indirect cost rate of 70%, a $500k project is only $294k of direct costs. If you have the PI's effort, fringe, and a student's effort and tuition to consider, and the project is three years, you are talking less than $100k per year to distribute. At my university, many PIs don't take any salary because this money is so little, and students and postdocs are so expensive. $100k direct annually won't even get you a postdoc for a year in Computer Science, and not much more than a student. You can likely look up your indirect ("facilities and administration") and fringe rates as most academic institutions publish them online.
If you are still concerned, you can see if your institution has a whistleblower option and let an internal group investigate. However, if they find no fault, you have to accept that you just don't know how grants are run and there is nothing wrong with that; you just are not privileged to know this information.
Please note that if any student or postdoc asked for information on a project that they are paid on, I would only be willing to give them the award number for their publications' acknowledgment section. I would never discuss spending with them or anyone who is not the PI. I even limit conversations with Co-PIs to the spending they oversee.
