From what I can see the four hex numbers in parenthesis are not of great value in sorting out the issue. Even if the numbers match other error codes reported on these sites they are not relevant. Only the first number 0x000000F4 and any error text is relevant.
The two important issues are:
1 the 0x000000F4 error code, and
2 the fact that XP fails to load intermittently with a noise that may be hard drive related.
As the failure is intermittent, the fault is unlikely to be a 'hard' error such as a hard drive connected as a slave with no master.
Intermittent failures in the boot process are more likely to be hardware related, such as a faulty memory or a hard drive read error.
The clicking sound suggests a hard drive error, such as a sector failing. Some hard drive failures happen slowly, rather than as a single catastrophic failure.
I noted that the application layer gateway service did not start on one occasion, but this is not enough to stop Windows starting. AFAIK this is not an essential service. This may just be a case of a non-essential service that did not load properly, also due to disk errors.
As a remote observer, my suggestion is that you have a hard drive sector that is failing and the error code seems to be consistent with this.
If this is the case, you could run hard drive tests for bad sectors (but don't use the repair option as an essential sector may be locked out).
If this is a failing sector that contains part of an essential Windows file, then a backup now before total failure would be a relatively simple protective measure.
A new hard drive of the same size or larger could be connected and a full drive copy i.e. a disk clone (not a partition copy) should be undertaken. Then change the boot sequence to boot to the new drive.
Hopefully others will comment, as my observations are by no means definitive !!!!